[
{
"id": "front-001",
"type": "title",
"section": "题名与出版信息",
"source_page": 1,
"source_ids": [
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"translation_ids": [
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"source": "Toward Market-Assisted AI: Cloud Inference for Streamed Data via Model Ensembles From Auctions",
"translation": "迈向市场辅助的人工智能：通过拍卖获得模型集成以服务流式数据的云端推理",
"notes": {
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},
{
"id": "front-002",
"type": "paragraph",
"section": "题名与出版信息",
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"source_ids": [
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"translation_ids": [
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],
"source": "Yining Zhang, Lei Jiao, Member, IEEE, Konglin Zhu, Xiaojun Lin, Fellow, IEEE, and Lin Zhang, Member, IEEE",
"translation": "Yining Zhang、Lei Jiao（IEEE 会员）、Konglin Zhu、Xiaojun Lin（IEEE 会士）、Lin Zhang（IEEE 会员）",
"notes": {
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{
"id": "front-003",
"type": "reference-note",
"section": "题名与出版信息",
"source_page": 1,
"source_ids": [
"front-003"
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"zh-front-003"
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"source": "IEEE TRANSACTIONS ON NETWORKING, VOL. 33, NO. 2, APRIL 2025. Digital Object Identifier 10.1109/TNET.2024.3505252",
"translation": "刊于 IEEE Transactions on Networking，第 33 卷，第 2 期，2025 年 4 月，本文页码 793–806。数字对象标识符（DOI）：10.1109/TNET.2024.3505252。",
"notes": {
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{
"id": "front-004",
"type": "reference-note",
"section": "题名与出版信息",
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"source": "Received 24 January 2024; revised 8 October 2024; accepted 17 November 2024; approved by IEEE TRANSACTIONS ON NETWORKING Editor G. Iosifidis. Date of publication 5 December 2024; date of current version 18 April 2025.",
"translation": "2024 年 1 月 24 日收稿；2024 年 10 月 8 日修回；2024 年 11 月 17 日录用；由 IEEE Transactions on Networking 编辑 G. Iosifidis 审定。2024 年 12 月 5 日在线发表；2025 年 4 月 18 日为当前版本日期。",
"notes": {
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},
{
"id": "front-005",
"type": "reference-note",
"section": "题名与出版信息",
"source_page": 1,
"source_ids": [
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"zh-front-005"
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"source": "This work was supported in part by the National Key Research and Development Program of China under Grant 2023YFB2704500; in part by Beijing Natural Science Foundation under Grant 4222033 and Grant 9232008; in part by Beijing Advanced Innovation Center for Future Blockchain and Privacy Computing; and in part by U.S. National Science Foundation under Grant CNS-2047719, Grant CNS-2225949, Grant CNS-2113893, and Grant CNS-2225950. (Corresponding authors: Lei Jiao; Konglin Zhu.)",
"translation": "本工作部分受中国国家重点研发计划资助（项目号 2023YFB2704500）；部分受北京市自然科学基金资助（项目号 4222033、9232008）；部分受北京未来区块链与隐私计算高精尖创新中心资助；部分受美国国家科学基金会资助（项目号 CNS-2047719、CNS-2225949、CNS-2113893、CNS-2225950）。（通信作者：Lei Jiao；Konglin Zhu。）",
"notes": {
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},
{
"id": "front-006",
"type": "reference-note",
"section": "题名与出版信息",
"source_page": 1,
"source_ids": [
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"translation_ids": [
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"source": "Yining Zhang, Konglin Zhu, and Lin Zhang are with the School of Artificial Intelligence, Beijing University of Posts and Telecommunications, Beijing 100876, China. Lei Jiao is with the Center for Cyber Security and Privacy, University of Oregon, Eugene, OR 97403 USA. Xiaojun Lin is with Elmore Family School of Electrical and Computer Engineering, Purdue University, West Lafayette, IN 47907 USA. This article has supplementary downloadable material available at https://doi.org/10.1109/TON.2024.3505252, provided by the authors.",
"translation": "Yining Zhang、Konglin Zhu 与 Lin Zhang 就职于北京邮电大学人工智能学院（中国北京 100876）。Lei Jiao 就职于俄勒冈大学网络空间安全与隐私中心（美国俄勒冈州尤金市 97403）。Xiaojun Lin 就职于普渡大学 Elmore 家族电气与计算机工程学院（美国印第安纳州西拉法叶市 47907）。本文附有作者提供的可下载补充材料，见 https://doi.org/10.1109/TON.2024.3505252。",
"notes": {
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},
{
"id": "front-007",
"type": "abstract",
"section": "题名与出版信息",
"source_page": 1,
"source_ids": [
"front-007"
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"translation_ids": [
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"source": "Abstract—While ensemble methods can tackle concept drifts, obtaining pretrained models and conducting ensemble learning upon streamed data impose fundamental challenges, including the dynamic balance between system overhead and inference accuracy in uncertain system environments, and the interlacement between desired economic properties and long-term participation. In this paper, we propose the joint optimization which enables service providers to obtain models via repetitive auctions from the model providers and conduct ensemble methods online in a cost-efficient manner. We design polynomial-time online algorithms to solve the underlying non-linear mixed-integer social cost minimization problem, involving bid selection, payment allocation, model hosting, and ensemble model-weight adaption. We further rigorously prove the performance guarantees with our approach, such as the sub-linear dynamic regret for the bidding cost, the sub-linear dynamic fit for the long-term participation constraint, the truthfulness and the individual rationality for the auctions, the upper bound for ensemble inference loss, and the parameterized-constant competitive ratio for the long-term social cost. Through extensive trace-driven evaluations under real-world settings, we have validated the significant advantages of our approach over multiple baselines and state-of-the-art algorithms.",
"translation": "摘要——集成方法虽能应对概念漂移，但在流式数据上获取预训练模型并开展集成学习仍面临根本性挑战：一是不确定的系统环境中系统开销与推理精度之间的动态平衡，二是所期望的经济性质与长期参与之间的交织关系。本文提出一种联合优化方案，使服务提供方能够通过重复拍卖从模型提供方处获得模型，并以成本高效的方式在线开展集成学习。我们设计了多项式时间的在线算法，以求解底层的非线性混合整数社会成本最小化问题，该问题涉及投标选择、支付分配、模型托管以及集成模型权重自适应。我们进一步严格证明了该方案的一系列性能保证，包括投标成本的次线性动态遗憾、长期参与约束的次线性动态拟合、拍卖的真实性与个体理性、集成推理损失的界，以及长期社会成本的参数化常数竞争比。通过在真实设定下的大量轨迹驱动评估，我们验证了所提方法相对多种基线方法与前沿算法的显著优势。",
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},
{
"id": "front-008",
"type": "paragraph",
"section": "题名与出版信息",
"source_page": 1,
"source_ids": [
"front-008"
],
"translation_ids": [
"zh-front-008"
],
"source": "Index Terms—Ensemble learning, inference, data stream, cloud computing, online optimization, auction.",
"translation": "关键词——集成学习、推理、数据流、云计算、在线优化、拍卖。",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "fig-1-caption",
"type": "caption",
"section": "第一节 引言",
"source_page": 1,
"source_ids": [
"fig-1-caption"
],
"translation_ids": [
"zh-fig-1-caption"
],
"source": "Fig. 1. System scenario.",
"translation": "图 1 系统场景。",
"notes": {
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"origin": "source"
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},
{
"id": "sec1-heading",
"type": "heading",
"section": "第一节 引言",
"source_page": 1,
"source_ids": [
"sec1-heading"
],
"translation_ids": [
"zh-sec1-heading"
],
"source": "I. INTRODUCTION",
"translation": "第一节 引言",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "sec1-001",
"type": "paragraph",
"section": "第一节 引言",
"source_page": 1,
"source_ids": [
"sec1-001"
],
"translation_ids": [
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"source": "It is very common for cloud services to perform machine learning inference in real time upon requests from end users [1], [2]. Often, as time goes, the inference accuracy of the service provider's model may vary or even irreversibly decrease because of concept drifts [3], [4], i.e., the existing model can no longer infer the best label for the data. One solution is to retrain or dynamically update the model as concept drifts are detected. However, for real-time inference on users' request streams, this could be infeasible due to insufficient training data, long delay of training, or prohibitive computation overhead. In contrast, ensemble methods [5], [6], [7] can combine multiple complementary pretrained models, including the service provider's model and those provided by others (which we can call model providers), to achieve better accuracy and resilience against concept drifts without detecting them explicitly, thus providing an intriguing alternative.",
"translation": "云服务根据终端用户的请求实时执行机器学习推理，这是十分常见的做法 [1], [2]。但随时间推移，服务提供方模型的推理精度往往会发生波动，甚至因概念漂移而不可逆地下降 [3], [4]——所谓概念漂移，即既有模型已无法为数据推断出最佳标签。一种解决办法是在检测到概念漂移时重新训练或动态更新模型；然而，对于用户请求流上的实时推理，这可能因训练数据不足、训练时延过长或计算开销过高而不可行。相比之下，集成方法 [5], [6], [7] 能够把多个互补的预训练模型（既包括服务提供方自己的模型，也包括他方——我们称之为模型提供方——提供的模型）组合起来，在不显式检测概念漂移的前提下取得更好的精度与抗漂移能力，因而提供了一条颇具吸引力的替代路径。",
"notes": {
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},
{
"id": "sec1-002",
"type": "paragraph",
"section": "第一节 引言",
"source_page": 1,
"source_ids": [
"sec1-002"
],
"translation_ids": [
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],
"source": "In fact, the service provider can engage in model transactions through AI model marketplaces with model providers [8], [9], [10], [11]. To incentivize the model providers to contribute their models, a monetizing mechanism is needed. Some AI marketplaces adopt direct pricing [12], [13], which can be less ideal due to the risk of mispricing [14], the lack of market efficiency, and the inability to adapt to real-time demand and supply. Auctions can address these disadvantages. In this paper, we advocate an auction-based approach, where the service provider can be the auctioneer and purchase models from the model providers that act as the bidders.",
"translation": "事实上，服务提供方可以通过 AI 模型市场与模型提供方进行模型交易 [8], [9], [10], [11]。为激励模型提供方贡献其模型，需要有变现机制。部分 AI 市场采用直接定价 [12], [13]，但这并不理想：存在定价失误的风险 [14]、缺乏市场效率，且无法适应实时的供需变化。拍卖可以弥补这些不足。本文主张采用基于拍卖的方案：服务提供方充当拍卖人，向作为竞标者的模型提供方购买模型。",
"notes": {
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},
{
"id": "sec1-003",
"type": "paragraph",
"section": "第一节 引言",
"source_page": 1,
"source_ids": [
"sec1-003"
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"translation_ids": [
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"source": "Unfortunately, designing such an auction and control mechanism faces multiple challenges, as the service provider has to optimally operate the system both by assembling the ensemble and performing inference in the \"front end\", and by jointly conducting auctions and managing models in the \"back end\". The first is how to control the dynamic balance, in an online manner, between system overhead and inference accuracy upon users' data stream as the system operates continuously. Combining more models to form the ensemble may lead to better inference accuracy, but having too many models could incur excessive model hosting cost. Whether to discard a model is also tricky as it involves \"time-coupled\" decisions [15]—keeping the model local could save the model downloading cost from model providers if this model is needed in the future, but it could cause waste if this model is not needed later. That is, the models need to be selected and deployed in terms of not only the incurred cost, but also the contribution to the inference loss of the ensemble. The unknown and unpredictable time-varying system environments and concept drifts, as well as the nonlinearity of both the cost and the inference loss functions, all escalate the difficulty and the complexity of the problem.",
"translation": "遗憾的是，设计这样的拍卖与控制机制面临多重挑战：服务提供方既要通过在“前端”组装集成并执行推理来最优地运行系统，又要在“后端”联合开展拍卖并管理模型。第一个挑战是：在系统持续运行的过程中，如何在线控制用户在数据流上的系统开销与推理精度之间的动态平衡。组合更多模型构成集成可能带来更高的推理精度，但模型过多会带来过高的模型托管成本。是否丢弃某个模型同样棘手，因为这涉及“时间耦合”的决策 [15]——把模型保留在本地，可以在将来需要它时省下向模型提供方下载模型的成本；但若以后用不到，保留就成了浪费。也就是说，模型的选择与部署不只要看当期成本，还要看它对集成推理损失的贡献。未知且难以预测的时变系统环境与概念漂移，加上成本函数与推理损失函数的非线性，共同抬高了问题的难度与复杂度。",
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{
"id": "note-sec1-01",
"type": "paragraph",
"section": "第一节 引言",
"source_page": 1,
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"translation": "**为什么需要“后端＋前端”两段式结构。** 作者把系统切成两半：前端决定“用哪些模型投票、权重多少”（影响精度），后端决定“跟谁买模型、付多少钱、留不留”（影响成本）。这个切分是全文算法的骨架——算法 1–3 服务后端拍卖，算法 4 决定托管，算法 5 服务前端集成。读者若只记一件事，就记这个分工。",
"notes": {
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{
"id": "sec1-004",
"type": "paragraph",
"section": "第一节 引言",
"source_page": 2,
"source_ids": [
"sec1-004"
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"translation_ids": [
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"source": "The other challenge is how to design the repetitive auctions that attain the desired economic properties, including truthfulness (i.e., a bidder maximizes its utility by not cheating about the bidding price) and individual rationality (i.e., a bidder has no loss on utility regardless of the auction outcome). The well-known Vickrey-Clarke-Groves (VCG) auctions [16] often require exactly solving the underlying social cost problem which can be intractable in our setting. The service provider may also desire to incentivize the long-term participation [17], [18], [19], [20] of model providers across auctions. Without a sufficient number of participants, the service provider may struggle to gather good models; if a model provider rarely wins in the auctions, it may quit permanently. Consequently, selecting the winning bids needs to consider not only the current auction but also existing and future auctions in the long term—buying a bid now could be unnecessary if the future bids end up cheaper or offer better models; but not buying it now could force us to buy bids later, even if they turn out to be costly or inferior. This interlacement between long-term participation and economic properties has not been typically studied previously.",
"translation": "另一个挑战是：如何设计重复拍卖以取得所期望的经济性质，包括真实性（即竞标者不谎报竞价时其效用最大）与个体理性（即无论拍卖结果如何，竞标者的效用都不会变差）。著名的 Vickrey-Clarke-Groves（VCG）拍卖 [16] 通常要求精确求解底层社会成本问题，而在本文设定下这可能是难解的。服务提供方还可能希望激励模型提供方在多次拍卖中的长期参与 [17], [18], [19], [20]。若参与者数量不足，服务提供方难以汇集优质模型；而若某个模型提供方在拍卖中很少获胜，它可能永久退出。因此，选择获胜投标不仅要考虑当前这场拍卖，还要考虑长期意义上的既有与未来拍卖——现在买下一份投标，若将来的投标更便宜或模型更好，这笔支出就未必必要；但现在不买，又可能在将来被迫购买，即便那时价格高昂或模型较差。这种长期参与与经济性质之间的交织，此前通常未被研究。",
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},
{
"id": "sec1-005",
"type": "paragraph",
"section": "第一节 引言",
"source_page": 2,
"source_ids": [
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"translation_ids": [
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"source": "Existing research is not adequate for addressing the aforementioned challenges. The work in [21], [22], [23], [24], [25], and [26] studies ensemble methods, but generally neglects the system environment where such methods are executed. The work in [27], [28], [29], [30], [31], and [32] investigates ensemble learning specifically in cloud and/or edge environments, but neither targets an online and data streaming setting nor accounts for the auction mechanisms. The work on AI model markets [12], [13], [33], [34], [35], [36] also falls short, either overlooking economic interactions or lacking consideration of ensembles or the joint optimization of system performance. See Section VII for our more detailed discussions.",
"translation": "现有研究不足以应对上述挑战。[21], [22], [23], [24], [25], [26] 研究集成方法，但普遍忽略了这类方法所运行的系统环境。[27], [28], [29], [30], [31], [32] 专门研究云和/或边缘环境下的集成学习，但既未面向在线与数据流式设定，也未考虑拍卖机制。关于 AI 模型市场的工作 [12], [13], [33], [34], [35], [36] 同样存在不足：或忽视经济交互，或未考虑集成，或缺少对系统性能的联合优化。更详细的讨论见第七节。",
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},
{
"id": "sec1-006",
"type": "paragraph",
"section": "第一节 引言",
"source_page": 2,
"source_ids": [
"sec1-006"
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"translation_ids": [
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],
"source": "In this paper, we model the joint cost and inference structure of an auction-assisted ensemble-learning service for streamed data samples. We formulate a social cost minimization problem over time for the service provider, considering model hosting cost, model downloading cost, ensemble inference loss, payment flows, and the utility of model providers. Our formulation features arbitrarily time-varying inputs, time-coupled switching-cost terms, and long-term constraints, capturing all the aforementioned challenges. Our problem is a non-linear mixed-integer program, and is unsurprisingly NP-hard.",
"translation": "本文对面向流式数据样本的“拍卖辅助集成学习服务”的联合成本与推理结构进行建模。我们为服务提供方形式化了一个跨时间的社会成本最小化问题，其中计入模型托管成本、模型下载成本、集成推理损失、支付流以及模型提供方的效用。我们的建模具有三个特征：输入可任意时变、切换成本项存在时间耦合、以及长期约束——从而覆盖了前述全部挑战。该问题是一个非线性混合整数规划，且不出所料是 NP 难的。",
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},
{
"id": "note-sec1-02",
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"section": "第一节 引言",
"source_page": 2,
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"translation": "**问题难在哪里（为后面的算法做铺垫）。** 三个特征各自对应一种难度：
**① 输入任意时变** ⇒ 无法预知未来，只能在线决策，于是需要“动态遗憾/动态拟合”这类相对离线最优的度量；
**② 切换成本时间耦合** ⇒ 今天保留一个模型，会改变明天的可选集合与成本，决策不可逐期分解（这是算法 4 用“懒惰切换”的理由）；
**③ 长期约束** ⇒ 例如“长期参与”要求跨期满足，不能由单期最优保证（这是算法 1 把长期约束用近似项吸进目标的理由）。",
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},
{
"id": "sec1-007",
"type": "paragraph",
"section": "第一节 引言",
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"source": "We propose a universal mechanism to select winning bids, allocate payments, host models, and conduct ensemble learning, regardless of the types of the models that comprise the ensemble. To that end, we design a holistic set of polynomial-time online algorithms that work together. In each auction, first, given the model hosting decisions, we design the Online Fractional Algorithm (i.e., Algorithm 1) to make fractional bid selections based on alternate descent-ascent primal-dual steps for a reformulation that absorbs the long-term constraint into the objective by a well-designed proximal term [37], [38]. Next, we design the Randomized Rounding Algorithm (i.e., Algorithm 2) to convert such fractional decisions into more tangible integer bid selections in a randomized manner without violating the residual constraints. Further, we design the Payment Allocation Algorithm (i.e., Algorithm 3) to replace VCG and calculate payments to the bids based on the actual fractional decision and bidding price and the envisaged fractional decisions with alternative bidding prices. Then, we design the Model Hosting Algorithm (i.e., Algorithm 4) that ties the repetitive auctions over time and invokes Algorithms 1 and 2 to select and deploy models via comparing in real time the most recent downloading cost of switching from previous models to the current models versus the cumulative hosting cost of retaining the current models since the last switch operation. Finally, we design the Ensemble Learning Algorithm (i.e., Algorithm 5) to combine the inference results of the models from Algorithm 4 as a weighted sum to produce the joint result for each data sample, while updating the weights in an exponential manner as data samples arrive [39].",
"translation": "我们提出一套通用机制，用于选择获胜投标、分配支付、托管模型并开展集成学习，且不依赖于构成集成的模型类型。为此，我们设计了一组彼此配合的、多项式时间的在线算法。在每一场拍卖中：首先，在给定模型托管决策的前提下，我们设计在线分数算法（即算法 1），通过交替的下降–上升原始–对偶步骤进行分数式投标选择；该步骤针对一个重述问题，其中用精心设计的近似项把长期约束吸收进目标函数 [37], [38]。其次，我们设计随机舍入算法（即算法 2），以随机方式把上述分数决策转换为更具体的整数投标选择，同时不违反剩余约束。再次，我们设计支付分配算法（即算法 3）以取代 VCG：它依据实际的分数决策与竞价、以及“以替代竞价设想出的”分数决策来计算向各投标的支付。随后，我们设计模型托管算法（即算法 4），它把跨时间的重复拍卖串联起来，并调用算法 1 与算法 2 来选择与部署模型——做法是实时比较“从先前模型切换到当前模型的最新下载成本”与“自上次切换操作以来保留当前模型的累计托管成本”。最后，我们设计集成学习算法（即算法 5），把算法 4 所选模型的推理结果以加权和方式合并，为每个数据样本产生联合结果，并随着数据样本到达以指数方式更新权重 [39]。",
"notes": {
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{
"id": "note-sec1-03",
"type": "paragraph",
"section": "第一节 引言",
"source_page": 2,
"source_ids": [
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"translation": "**五个算法一句话各自做什么。** 这一段是全文的“算法地图”，建议先记住：
**算法 1**（在线分数算法）：本轮该买哪些投标，先允许“买 0.7 份”，用原始–对偶交替更新求解。
**算法 2**（随机舍入）：把 0.7 份变成“买/不买”，且保持期望不变、不破坏约束。
**算法 3**（支付分配）：算钱。用“实际决策”与“去掉你的替代决策”之差来决定付给你多少——这是替代 VCG 的关键技巧。
**算法 4**（模型托管）：决定哪些模型留在本地，用“切换下载成本 vs 继续托管的累计成本”比较，即“懒惰切换”。
**算法 5**（集成学习）：把各模型的投票按权重加权求和，权重按指数更新（Hedge）。",
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},
{
"id": "sec1-008",
"type": "paragraph",
"section": "第一节 引言",
"source_page": 2,
"source_ids": [
"sec1-008"
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"translation_ids": [
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"source": "We provide a thorough analysis of our proposed algorithms by formally proving a series of theorems. We exhibit that the dynamic regret and the dynamic fit [38], [40] are sub-linear, i.e., as the total number of time slots grows, the difference between the time-averaged bidding cost incurred by our online approach and its time-averaged offline optimum gradually vanishes, so does the time-averaged violation of the long-term participation. We show that truthfulness and individual rationality are met in expectation. We further imply that the inference loss generated by our ensemble method is upper-bounded by a constant times that generated by the single best model out of our selected models. Based on that, we establish the competitiveness, i.e., the social cost over time incurred by our online approach is no greater than a constant times the sum of the offline optimal cost over time plus the cumulative inference loss of the single best model for each time slot.",
"translation": "我们通过严格证明一系列定理，对所提算法进行了透彻分析。我们证明动态遗憾与动态拟合 [38], [40] 都是次线性的：随着时隙总数增长，在线方法产生的时间平均投标成本与其时间平均离线最优值之间的差距逐渐消失，长期参与约束的时间平均违反量同样如此。我们证明真实性与个体理性在期望意义下成立。我们进一步说明：集成方法产生的推理损失，被“所选模型中单个最佳模型”所产生损失的常数倍所上界。基于此，我们建立了竞争性：在线方法产生的长期社会成本，不超过“离线最优成本的时间累加”加上“每个时隙单个最佳模型的推理损失累加”的常数倍。",
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},
{
"id": "sec1-009",
"type": "paragraph",
"section": "第一节 引言",
"source_page": 2,
"source_ids": [
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"translation_ids": [
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"source": "Finally, we implement and test a classification service upon multiple real-world time-lapse data streams [41], [42] and benchmark datasets [43], [44], with up to 64 model providers at geographically-distributed clouds worldwide [45], [46] under realistic settings [17], [20], [47], [48]. Our evaluations reveal the following results: (i) Compared to the baselines of the Random method, the Greedy method, and the state-of-the-art-based DTEL+ and DES+ method, our approach reduces the long-term social cost on average by 70%, 37%, 35%, and 46%, respectively, with the empirical competitive ratio of 2.1 ∼ 2.7; (ii) Our approach achieves truthfulness and individual rationality in every auction; (iii) Our approach incurs the lowest dynamic regret and the lowest dynamic fit, which only grow slowly with time; (iv) Our approach attains an inference accuracy of about 2% ∼ 9% higher than DTEL+ and DES+; (v) Most of our algorithms complete in a few seconds for each auction with the delay-insensitive payment calculated in less than a minute, meeting the needs in reality.",
"translation": "最后，我们在多条真实世界的时移数据流 [41], [42] 与基准数据集 [43], [44] 上实现并测试了一个分类服务：在真实设定 [17], [20], [47], [48] 下，涉及全球地理分布的云上最多 64 个模型提供方 [45], [46]。评估得到如下结果：(i) 与随机方法、贪心方法、以及基于前沿工作的 DTEL+ 与 DES+ 三种基线相比，本方法把长期社会成本平均降低 70%、37%、35% 与 46%，经验竞争比为 2.1 ∼ 2.7；(ii) 本方法在每一场拍卖中都满足真实性与个体理性；(iii) 本方法取得最低的动态遗憾与最低的动态拟合，且二者随时间只缓慢增长；(iv) 本方法的推理精度比 DTEL+ 与 DES+ 高约 2% ∼ 9%；(v) 在每场拍卖中，本方法的大多数算法在数秒内完成，对时延不敏感的支付计算在不到一分钟内完成，满足现实需求。",
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"id": "sec2-heading",
"type": "heading",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
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"translation_ids": [
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"source": "II. MODEL AND PROBLEM FORMULATION",
"translation": "第二节 模型与问题形式化",
"notes": {
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{
"id": "sec2-sub-a",
"type": "heading",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"sec2-sub-a"
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"translation_ids": [
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"source": "A. System Modeling",
"translation": "A. 系统建模",
"notes": {
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{
"id": "sec2-001",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"sec2-001"
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"translation_ids": [
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"source": "We summarize all our major notations in Table I.",
"translation": "我们在表 I 中汇总了本文的主要符号。",
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{
"id": "table-1",
"type": "table",
"section": "第二节 模型与问题形式化",
"source_page": 3,
"source_ids": [
"table-1"
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"translation_ids": [
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"source": "**TABLE I — NOTATIONS**\n\n| Notation | Meaning |\n|---|---|\n| $\\mathcal T=\\{1,2,\\dots,T\\}$ | Set of consecutive time slots |\n| $\\mathcal M^t=\\{1,2,\\dots,M^t\\}$ | Set of data samples arriving in time slot $t$ |\n| $a^t_m$, $b^t_m$ | Feature values and ground-truth label of data sample $m$ |\n| $\\mathcal N=\\{1,2,\\dots,N\\}$ | Set of model providers (each offers one model) |\n| $h^t_n(\\cdot)$ | Decision function of the model offered by provider $n$ |\n| $h^t(\\cdot)$ | Decision function of the service provider's own model |\n| $c^t_n$ | Bidding price charged by bid $n$ |\n| $p^t_n$ | Payment made to bid $n$ |\n| $u^t_n$ | Cost of downloading model $n$ from provider $n$ |\n| $v^t_n$ | Cost of hosting model $n$ at the service provider |\n| $e^t$ | Cost of hosting the service provider's own model |\n| $\\Delta^t_n\\in\\{0,1\\}$ | Whether model $n$ at $t$ differs from that at $t-1$ |\n| $W\\ge 1$ | Minimum number of models to host for ensemble learning |\n| $Q^t\\ge 0$ | Purchase budget: maximum number of models purchasable at $t$ |\n| $\\phi_n\\in[0,1]$ | Participation threshold of provider $n$ |\n| $x^t_n\\in\\{0,1\\}$ | Whether model $n$ wins the auction at $t$ |\n| $y^t_n\\in\\{0,1\\}$ | Whether model $n$ is hosted and deployed at $t$ |\n| $z^t\\in\\{0,1\\}$ | Whether the service provider hosts its own model at $t$ |\n| $\\alpha^t_{n,m}\\in[0,1]$ | Weight of purchased model $n$ for data sample $m$ |\n| $\\beta^t_m\\in[0,1]$ | Weight of the service provider's own model for sample $m$ |\n| $\\hat b^t_m$ | Joint inference result for data sample $m$ |\n| $l(\\cdot,\\cdot)$ | Loss function (squared loss) |",
"translation": "**表 I — 符号表**\n\n| 符号 | 含义 |\n|---|---|\n| $\\mathcal T=\\{1,2,\\dots,T\\}$ | 连续时隙的集合 |\n| $\\mathcal M^t=\\{1,2,\\dots,M^t\\}$ | 时隙 $t$ 内到达的数据样本集合 |\n| $a^t_m$、$b^t_m$ | 数据样本 $m$ 的特征值与真实标签 |\n| $\\mathcal N=\\{1,2,\\dots,N\\}$ | 模型提供方集合（每家提供一个模型） |\n| $h^t_n(\\cdot)$ | 提供方 $n$ 所提供模型的决策函数 |\n| $h^t(\\cdot)$ | 服务提供方自有模型的决策函数 |\n| $c^t_n$ | 投标 $n$ 的竞价 |\n| $p^t_n$ | 向投标 $n$ 支付的金额 |\n| $u^t_n$ | 从提供方 $n$ 下载模型 $n$ 的成本 |\n| $v^t_n$ | 在服务提供方处托管模型 $n$ 的成本 |\n| $e^t$ | 托管服务提供方自有模型的成本 |\n| $\\Delta^t_n\\in\\{0,1\\}$ | 模型 $n$ 在 $t$ 与 $t-1$ 是否不同 |\n| $W\\ge 1$ | 为集成学习所需托管的最少模型数 |\n| $Q^t\\ge 0$ | 购买预算：$t$ 时刻最多可购买的模型数 |\n| $\\phi_n\\in[0,1]$ | 提供方 $n$ 的参与阈值 |\n| $x^t_n\\in\\{0,1\\}$ | 模型 $n$ 在 $t$ 是否赢得拍卖 |\n| $y^t_n\\in\\{0,1\\}$ | 模型 $n$ 在 $t$ 是否被托管与部署 |\n| $z^t\\in\\{0,1\\}$ | 服务提供方在 $t$ 是否托管自有模型 |\n| $\\alpha^t_{n,m}\\in[0,1]$ | 数据样本 $m$ 上购买模型 $n$ 的权重 |\n| $\\beta^t_m\\in[0,1]$ | 数据样本 $m$ 上自有模型的权重 |\n| $\\hat b^t_m$ | 数据样本 $m$ 的联合推理结果 |\n| $l(\\cdot,\\cdot)$ | 损失函数（平方损失） |",
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"id": "note-table1",
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"section": "第二节 模型与问题形式化",
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"translation": "**关于表 I（符号表）的说明。** 原文的表 I 在 PDF 中是嵌入的位图，其文字无法抽取（用表格线抽取器得到的单元格全为空）。上面的符号表是我依据原文正文与公式（第二节 A、B 两小节）中给出的定义重建的，不是原文表格的逐字复制；同时我把原文表格图像作为 `assets/figures/table-1-original.png` 一并保留，便于逐项核对。凡符号定义，请以原文图像与正文为准。",
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"id": "sec2-002",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
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"translation_ids": [
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"source": "**Machine Learning Service:** We consider a machine learning service that continuously conducts inference upon a stream of data samples submitted by the end users. This machine learning service can be provisioned and operated by a service provider in the service provider's own data center or a public cloud. The data samples arrive dynamically over a series of consecutive time slots $\\mathcal{T}=\\{1,2,\\dots,T\\}$. For the time slot $t\\in\\mathcal{T}$, we use $\\mathcal{M}^t=\\{1,2,\\dots,M^t\\}$ to index the data samples that arrive during $t$. For the data sample $m\\in\\mathcal{M}^t$, we represent it as $\\{a^t_m,b^t_m\\}$, where $a^t_m$ refers to its feature values and $b^t_m$ refers to its ground-truth label.",
"translation": "**机器学习服务：** 我们考虑一个机器学习服务，它持续地对终端用户提交的数据样本流执行推理。该服务可以由服务提供方在其自有数据中心或公有云上供给与运营。数据样本在一系列连续时隙 $\\mathcal{T}=\\{1,2,\\dots,T\\}$ 上动态到达。对于时隙 $t\\in\\mathcal{T}$，我们用 $\\mathcal{M}^t=\\{1,2,\\dots,M^t\\}$ 索引在 $t$ 期间到达的数据样本。对于数据样本 $m\\in\\mathcal{M}^t$，我们把它表示为 $\\{a^t_m,b^t_m\\}$，其中 $a^t_m$ 是其特征值，$b^t_m$ 是其真实标签。",
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"id": "sec2-003",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
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"source": "**Models and Costs:** Besides its own model, the service provider can purchase models from the model providers, denoted as $\\mathcal{N}=\\{1,2,\\dots,N\\}$, via the auction market as elaborated below and then download the purchased models for the local deployment. We consider each model provider offers one model; a model provider that offers multiple models can be treated as multiple \"virtual\" model providers. We use $u^t_n$ to denote the cost (e.g., traffic, delay) of downloading the model from the model provider $n\\in\\mathcal{N}$, i.e., the model $n$, at the time slot $t$, and use $v^t_n$ to denote the cost (e.g., resource, energy consumption) of hosting the model $n$ at the service provider's facility at $t$. A model provider may offer different models as time goes, so we use $\\Delta^t_n\\in\\{1,0\\}$ to imply whether or not the model $n$ at $t$ stays the same as at $t-1$. We also use $e^t$ to denote the cost of hosting the service provider's own model at $t$. Without loss of generality, for the ensemble learning to be described next, we envisage that the service provider wants to host a minimum number $W\\ge 1$ of models at any $t$, where $W$ is set based on the needs and capacity of the service provider.",
"translation": "**模型与成本：** 除自有模型外，服务提供方还可以通过下文详述的拍卖市场，从记为 $\\mathcal{N}=\\{1,2,\\dots,N\\}$ 的模型提供方处购买模型，然后下载所购模型用于本地部署。我们假定每个模型提供方提供一个模型；若某提供方提供多个模型，可将其视为多个“虚拟”模型提供方。我们用 $u^t_n$ 表示在时隙 $t$ 从模型提供方 $n\\in\\mathcal{N}$（即模型 $n$）下载模型的成本（例如流量、时延），并用 $v^t_n$ 表示在 $t$ 于服务提供方设施处托管模型 $n$ 的成本（例如资源、能耗）。模型提供方可能随时间提供不同的模型，因此我们用 $\\Delta^t_n\\in\\{1,0\\}$ 表示 $t$ 时刻的模型 $n$ 是否与 $t-1$ 时刻相同。我们另用 $e^t$ 表示在 $t$ 托管服务提供方自有模型的成本。不失一般性，为便于后文所述的集成学习，我们设想服务提供方希望在任意 $t$ 都至少托管 $W\\ge 1$ 个模型，其中 $W$ 依据服务提供方的需求与容量设定。",
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"section": "第二节 模型与问题形式化",
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"translation": "**三个成本符号的分工（后面反复出现）。** $u^t_n$ 是下载成本（一次性，只在需要新模型时发生）；$v^t_n$ 是托管成本（按期发生，只要模型留着就付）；$e^t$ 是自有模型的托管成本（不随 $\\mathcal N$ 变化）。$\\Delta^t_n$ 是“模型是否换代”的指示符，它把“下载成本要不要付”与“模型是否变化”绑定：只有当供应商换了模型（$\\Delta^t_n=1$）或是首次部署（$y^t_n-y^{t-1}_n=1$）时，才付出下载成本。",
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"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
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"translation_ids": [
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"source": "**Model Auctions:** The service provider acts as the auctioneer, and the model providers act as the bidders. At each time slot $t$, the auctioneer conducts an auction, as shown in Fig. 2:",
"translation": "**模型拍卖：** 服务提供方充当拍卖人，模型提供方充当竞标者。在每个时隙 $t$，拍卖人都会举行一场拍卖，如图 2 所示：",
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"source": "**Step 1:** Each bidder $n$ submits a bid in the format of $\\{c^t_n,h^t_n(\\cdot),\\Delta^t_n\\}$. $c^t_n$ is the bidding price, i.e., the amount of money the bid wants to charge for selling the offered model; $h^t_n(\\cdot)$ is the decision function of the offered model; and $\\Delta^t_n$ has already been explained in the above.",
"translation": "**步骤 1：** 每个竞标者 $n$ 提交一份形如 $\\{c^t_n,h^t_n(\\cdot),\\Delta^t_n\\}$ 的投标。其中 $c^t_n$ 是竞价，即该投标为出售所提供模型而希望收取的金额；$h^t_n(\\cdot)$ 是所提供模型的决策函数；$\\Delta^t_n$ 已在上文解释。",
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"source": "**Step 2:** Collecting all the bids, the auctioneer decides the winning bids, the payment $p^t_n$ to be made to each winning bid $n$ (note that $p^t_n$ does not necessarily equals $c^t_n$), and notifies the bidders of the auction outcome.",
"translation": "**步骤 2：** 拍卖人收集全部投标后，决定获胜投标、以及向每个获胜投标 $n$ 支付的金额 $p^t_n$（注意 $p^t_n$ 未必等于 $c^t_n$），并把拍卖结果通知各竞标者。",
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"zh-sec2-li-03"
],
"source": "**Step 3:** The auctioneer downloads the models from the winning bidder's facilities if the same model was not previously downloaded or if the model provider offers a different model compared to the last time the model was downloaded from this model provider.",
"translation": "**步骤 3：** 若此前未下载过同一模型，或该模型提供方此次提供的模型与上次从该提供方下载时不同，拍卖人就从获胜竞标者的设施下载模型。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-li-04",
"type": "list-item",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"sec2-li-04"
],
"translation_ids": [
"zh-sec2-li-04"
],
"source": "**Step 4:** The auctioneer sends the payment to each winning bidder.",
"translation": "**步骤 4：** 拍卖人向每个获胜竞标者支付款项。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-005",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"sec2-005"
],
"translation_ids": [
"zh-sec2-005"
],
"source": "To decide the winning bids, the auctioneer needs to solve the social cost minimization problem, which will be described next. For the auction at $t$, the auctioneer has the budget $Q^t\\ge 0$, indicating the maximum number of models that can be purchased. To incentivize the long-term participation of model providers, we use $\\phi_n\\in[0,1]$ to imply the participation threshold [17], [18]. That is, across all the $T$ auctions, each model provider $n$ should win for no less than $T\\cdot\\phi_n$ times; otherwise, we consider that the model provider $n$ may quit the marketplace permanently. Step 4 may appear before Step 3, depending on the agreement in the market.",
"translation": "为决定获胜投标，拍卖人需要求解社会成本最小化问题，这将在后文描述。对于 $t$ 时刻的拍卖，拍卖人拥有预算 $Q^t\\ge 0$，表示最多可购买的模型数。为激励模型提供方的长期参与，我们用 $\\phi_n\\in[0,1]$ 表示参与阈值 [17], [18]。也就是说，在全部 $T$ 场拍卖中，每个模型提供方 $n$ 至少应获胜 $T\\cdot\\phi_n$ 次；否则我们视为该提供方可能永久退出市场。视市场约定不同，步骤 4 也可能出现在步骤 3 之前。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-006",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"sec2-006"
],
"translation_ids": [
"zh-sec2-006"
],
"source": "**Ensemble Learning:** At the time slot $t$, after deploying the models, the machine learning service employs ensemble learning to perform inference sequentially upon the data samples $\\mathcal{M}^t$ by combining the inference results of different models. This workflow is as follows, shown in Fig. 3.",
"translation": "**集成学习：** 在时隙 $t$，部署完模型之后，机器学习服务采用集成学习，通过合并不同模型的推理结果，对数据样本 $\\mathcal{M}^t$ 依次执行推理。该工作流如下，并见图 3。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-li-05",
"type": "list-item",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"sec2-li-05"
],
"translation_ids": [
"zh-sec2-li-05"
],
"source": "**Step 1:** The data sample $m\\in\\mathcal{M}^t$ from an end user arrives with its feature $a^t_m$. The machine learning service uses each purchased model $n$ and its own model, whose decision functions are $h^t_n(\\cdot)$ and $h^t(\\cdot)$, respectively, to make inference results $h^t_n(a^t_m)$ and $h^t(a^t_m)$.",
"translation": "**步骤 1：** 来自终端用户的数据样本 $m\\in\\mathcal{M}^t$ 与其特征 $a^t_m$ 一同到达。机器学习服务分别用每个已购买的模型 $n$ 与自有模型（其决策函数分别为 $h^t_n(\\cdot)$ 与 $h^t(\\cdot)$）产生推理结果 $h^t_n(a^t_m)$ 与 $h^t(a^t_m)$。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-li-06",
"type": "list-item",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"sec2-li-06"
],
"translation_ids": [
"zh-sec2-li-06"
],
"source": "**Step 2:** The joint inference result is then produced as $\\hat{b}^t_m=\\sum_n\\alpha^t_{n,m}h^t_n(a^t_m)+\\beta^t_mh^t(a^t_m)$, where $\\alpha^t_{n,m}$ is the weight for the purchased model $n$ upon the data sample $m$ and $\\beta^t_m$ is the weight for the service provider's own model upon the data sample $m$. $\\hat{b}^t_m$ is further sent back to the corresponding end user.",
"translation": "**步骤 2：** 随后产生联合推理结果 $\\hat{b}^t_m=\\sum_n\\alpha^t_{n,m}h^t_n(a^t_m)+\\beta^t_mh^t(a^t_m)$，其中 $\\alpha^t_{n,m}$ 是已购买模型 $n$ 在数据样本 $m$ 上的权重，$\\beta^t_m$ 是服务提供方自有模型在数据样本 $m$ 上的权重。$\\hat{b}^t_m$ 随后被送回对应的终端用户。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-li-07",
"type": "list-item",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"sec2-li-07"
],
"translation_ids": [
"zh-sec2-li-07"
],
"source": "**Step 3:** The ground-truth label $b^t_m$ arrives from the same end user.",
"translation": "**步骤 3：** 真实标签 $b^t_m$ 由同一终端用户返回。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-li-08",
"type": "list-item",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"sec2-li-08"
],
"translation_ids": [
"zh-sec2-li-08"
],
"source": "**Step 4:** The machine learning service updates the weights for all the models for the next data sample $m+1$.",
"translation": "**步骤 4：** 机器学习服务为下一个数据样本 $m+1$ 更新所有模型的权重。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-007",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"sec2-007"
],
"translation_ids": [
"zh-sec2-007"
],
"source": "The aforementioned process of conducting the inference first and receiving the ground truth afterward can capture many real-world applications such as ads recommendation systems [49], [50] and keyboard input methods [51]. Without loss of generality, we consider the squared loss function $l(\\cdot,\\cdot)$. Thus, we can denote the total cumulative loss incurred upon the entire data stream as $\\sum_t\\sum_m l(\\hat{b}^t_m,b^t_m)=\\sum_t\\sum_m((\\sum_n\\alpha^t_{n,m}h^t_n(a^t_m)+\\beta^t_mh^t(a^t_m))-b^t_m)^2$.",
"translation": "上述“先执行推理、之后才收到真实标签”的过程可以刻画许多真实应用，例如广告推荐系统 [49], [50] 与键盘输入法 [51]。不失一般性，我们考虑平方损失函数 $l(\\cdot,\\cdot)$。于是，整个数据流上产生的累计总损失可表示为 $\\sum_t\\sum_m l(\\hat{b}^t_m,b^t_m)=\\sum_t\\sum_m((\\sum_n\\alpha^t_{n,m}h^t_n(a^t_m)+\\beta^t_mh^t(a^t_m))-b^t_m)^2$。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec2-02",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 2,
"source_ids": [
"note-sec2-02"
],
"translation_ids": [
"zh-note-sec2-02"
],
"source": "",
"translation": "**为什么“先推理、后拿标签”这个顺序很关键。** 它意味着权重更新只能用已经观察到的样本，未来的标签不可知——这正是在线学习（Hedge 类算法）的设定，也是第 IV 节算法 5 只能做“事后更新”的原因。若顺序反过来（先见标签再推理），问题会退化为普通的监督学习，全文的遗憾/拟合分析就失去意义。",
"notes": {
"kind": "green",
"origin": "source"
}
},
{
"id": "sec2-008",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"sec2-008"
],
"translation_ids": [
"zh-sec2-008"
],
"source": "**Control Variables:** The service provider needs to make the following control decisions. We use $x^t_n\\in\\{1,0\\}$ to denote whether or not the model $n$ wins the auction at the time slot $t$. We use $y^t_n\\in\\{1,0\\}$ to denote whether or not the model $n$ is hosted and deployed by the machine learning service at the time slot $t$. We use $z^t\\in\\{1,0\\}$ to denote whether or not the machine learning service hosts and deploys its own model at the time slot $t$. We use $\\alpha^t_{n,m}\\in[0,1]$ to denote the weight of the purchased model $n$ for performing inference for the data sample $m$ at the time slot $t$. We use $\\beta^t_m\\in[0,1]$ to denote the weight of the service provider's own model for performing inference for the data sample $m$ at the time slot $t$. We also use $p^t_n\\ge 0$ to denote the payment made to the model provider $n$ at the time slot $t$.",
"translation": "**控制变量：** 服务提供方需要做出如下控制决策。我们用 $x^t_n\\in\\{1,0\\}$ 表示模型 $n$ 在时隙 $t$ 是否赢得拍卖；用 $y^t_n\\in\\{1,0\\}$ 表示模型 $n$ 在时隙 $t$ 是否被机器学习服务托管与部署；用 $z^t\\in\\{1,0\\}$ 表示机器学习服务在时隙 $t$ 是否托管与部署其自有模型；用 $\\alpha^t_{n,m}\\in[0,1]$ 表示在时隙 $t$ 为数据样本 $m$ 执行推理时已购模型 $n$ 的权重；用 $\\beta^t_m\\in[0,1]$ 表示在时隙 $t$ 为数据样本 $m$ 执行推理时服务提供方自有模型的权重。我们另用 $p^t_n\\ge 0$ 表示在时隙 $t$ 向模型提供方 $n$ 支付的金额。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-009",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"sec2-009"
],
"translation_ids": [
"zh-sec2-009"
],
"source": "**Cost of Auctioneer:** The cost incurred at the machine learning service at $t$ has the following components: (i) Cost of hosting models $\\sum_n v^t_n y^t_n+e^t z^t$; (ii) Cost of downloading models $\\sum_n(\\Delta^t_n u^t_n[y^t_n-y^{t-1}_n]^+ + u^t_n y^t_n(1-\\Delta^t_n))$, where $[\\cdot]^+=\\max\\{\\cdot,0\\}$; (iii) Payment made to bidders $\\sum_n x^t_n p^t_n$.",
"translation": "**拍卖人的成本：** 机器学习服务在 $t$ 时刻产生的成本包含以下各项：(i) 模型托管成本 $\\sum_n v^t_n y^t_n+e^t z^t$；(ii) 模型下载成本 $\\sum_n(\\Delta^t_n u^t_n[y^t_n-y^{t-1}_n]^+ + u^t_n y^t_n(1-\\Delta^t_n))$，其中 $[\\cdot]^+=\\max\\{\\cdot,0\\}$；(iii) 向竞标者支付的款项 $\\sum_n x^t_n p^t_n$。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec2-03",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"note-sec2-03"
],
"translation_ids": [
"zh-note-sec2-03"
],
"source": "",
"translation": "**下载成本为什么长这样（逐项拆解）。** $\\sum_n\\Delta^t_n u^t_n[y^t_n-y^{t-1}_n]^+$：仅当模型换代（$\\Delta^t_n=1$）且本时刻新托管了它（$y^t_n=1>y^{t-1}_n=0$）时，才付出一次下载成本。
再加 $\\sum_n u^t_n y^t_n(1-\\Delta^t_n)$：模型未换代（$\\Delta^t_n=0$）但仍被托管（$y^t_n=1$）时，仍需再下载一次（例如上一时刻未托管、本时刻要用）。
两条合起来就是“只有当模型在本地可用且是所需版本时，才不必付下载费”。$[\\cdot]^+$ 确保已托管过（$y^{t-1}_n=1$）时不会产生负成本。",
"notes": {
"kind": "blue",
"origin": "source"
}
},
{
"id": "sec2-010",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"sec2-010"
],
"translation_ids": [
"zh-sec2-010"
],
"source": "**Cost of Bidders:** The cost incurred at the model providers at $t$ refers to the cost of training or producing the model (i.e., bidding price) determined by each model provider, minus any payment received from the service provider: $\\sum_n x^t_n(c^t_n-p^t_n)$.",
"translation": "**竞标者的成本：** 模型提供方在 $t$ 时刻产生的成本，指各提供方为训练或产出模型所确定的成本（即竞价）减去其从服务提供方获得的支付：$\\sum_n x^t_n(c^t_n-p^t_n)$。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-sub-b",
"type": "heading",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"sec2-sub-b"
],
"translation_ids": [
"zh-sec2-sub-b"
],
"source": "B. Problem Formulation and Algorithmic Challenges",
"translation": "B. 问题形式化与算法挑战",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-011",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"sec2-011"
],
"translation_ids": [
"zh-sec2-011"
],
"source": "**Social Cost Minimization:** The social cost refers to the sum of the cost of the service provider and the cost of the model providers over time, plus the cumulative inference loss upon the entire data stream. We formulate the social cost minimization problem $\\mathcal{P}_0$ as follows. Note that the payment terms cancel one another, but the payments still need to be determined later to satisfy the desired economic properties.",
"translation": "**社会成本最小化：** 社会成本指服务提供方的成本与模型提供方的成本在时间上的总和，再加上整个数据流上的累计推理损失。我们如下形式化社会成本最小化问题 $\\mathcal{P}_0$。注意支付项彼此抵消，但为满足所期望的经济性质，支付金额仍需在后文确定。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-001",
"type": "equation",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"eq-001"
],
"translation_ids": [
"zh-eq-001"
],
"source": "$$\n\\begin{aligned}\n\\mathcal P_0:\\min\\;&\\sum_t\\sum_n x^t_n c^t_n+\\sum_t\\sum_n\\Delta^t_n u^t_n\\left[y^t_n-y^{t-1}_n\\right]^+\\\\\n&+\\sum_t\\sum_n y^t_n\\left(v^t_n+u^t_n(1-\\Delta^t_n)\\right)+\\sum_t e^t z^t\\\\\n&+\\sum_t\\sum_m\\Big(\\sum_n\\alpha^t_{n,m}h^t_n(a^t_m)+\\beta^t_mh^t(a^t_m)-b^t_m\\Big)^2,\n\\end{aligned} \\tag{1}\n$$",
"translation": "$$\n\\begin{aligned}\n\\mathcal P_0:\\min\\;&\\sum_t\\sum_n x^t_n c^t_n+\\sum_t\\sum_n\\Delta^t_n u^t_n\\left[y^t_n-y^{t-1}_n\\right]^+\\\\\n&+\\sum_t\\sum_n y^t_n\\left(v^t_n+u^t_n(1-\\Delta^t_n)\\right)+\\sum_t e^t z^t\\\\\n&+\\sum_t\\sum_m\\Big(\\sum_n\\alpha^t_{n,m}h^t_n(a^t_m)+\\beta^t_mh^t(a^t_m)-b^t_m\\Big)^2,\n\\end{aligned} \\tag{1}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-001a",
"type": "equation",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"eq-001a"
],
"translation_ids": [
"zh-eq-001a"
],
"source": "$$\n\\text{s.t. }\\sum_n y^t_n+z^t\\ge W,\\quad\\forall t\\in\\mathcal T, \\tag{1a}\n$$",
"translation": "$$\n\\text{s.t. }\\sum_n y^t_n+z^t\\ge W,\\quad\\forall t\\in\\mathcal T, \\tag{1a}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-001b",
"type": "equation",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"eq-001b"
],
"translation_ids": [
"zh-eq-001b"
],
"source": "$$\n\\sum_n x^t_n\\le Q^t,\\quad\\forall t\\in\\mathcal T, \\tag{1b}\n$$",
"translation": "$$\n\\sum_n x^t_n\\le Q^t,\\quad\\forall t\\in\\mathcal T, \\tag{1b}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-001c",
"type": "equation",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"eq-001c"
],
"translation_ids": [
"zh-eq-001c"
],
"source": "$$\n\\sum_n\\alpha^t_{n,m}+\\beta^t_m=1,\\quad\\forall m\\in\\mathcal M^t,\\ \\forall t\\in\\mathcal T, \\tag{1c}\n$$",
"translation": "$$\n\\sum_n\\alpha^t_{n,m}+\\beta^t_m=1,\\quad\\forall m\\in\\mathcal M^t,\\ \\forall t\\in\\mathcal T, \\tag{1c}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-001d",
"type": "equation",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"eq-001d"
],
"translation_ids": [
"zh-eq-001d"
],
"source": "$$\n\\alpha^t_{n,m}\\le y^t_n,\\quad\\forall n\\in\\mathcal N,\\ \\forall m\\in\\mathcal M^t,\\ \\forall t\\in\\mathcal T, \\tag{1d}\n$$",
"translation": "$$\n\\alpha^t_{n,m}\\le y^t_n,\\quad\\forall n\\in\\mathcal N,\\ \\forall m\\in\\mathcal M^t,\\ \\forall t\\in\\mathcal T, \\tag{1d}\n$$",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "eq-001e",
"type": "equation",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"eq-001e"
],
"translation_ids": [
"zh-eq-001e"
],
"source": "$$\n\\beta^t_m\\le z^t,\\quad\\forall m\\in\\mathcal M^t,\\ \\forall t\\in\\mathcal T, \\tag{1e}\n$$",
"translation": "$$\n\\beta^t_m\\le z^t,\\quad\\forall m\\in\\mathcal M^t,\\ \\forall t\\in\\mathcal T, \\tag{1e}\n$$",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "eq-001f",
"type": "equation",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"eq-001f"
],
"translation_ids": [
"zh-eq-001f"
],
"source": "$$\nx^t_n\\ge y^t_n,\\quad\\forall n\\in\\mathcal N,\\ \\forall t\\in\\mathcal T, \\tag{1f}\n$$",
"translation": "$$\nx^t_n\\ge y^t_n,\\quad\\forall n\\in\\mathcal N,\\ \\forall t\\in\\mathcal T, \\tag{1f}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-001g",
"type": "equation",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"eq-001g"
],
"translation_ids": [
"zh-eq-001g"
],
"source": "$$\n\\frac{1}{T}\\sum_t x^t_n\\ge\\phi_n,\\quad\\forall n\\in\\mathcal N,\\qquad\\text{var. }x^t_n,y^t_n,z^t\\in\\{0,1\\},\\ \\alpha^t_{n,m},\\beta^t_m\\in[0,1],\\quad\\forall n\\in\\mathcal N,\\ \\forall m\\in\\mathcal M^t,\\ \\forall t\\in\\mathcal T. \\tag{1g}\n$$",
"translation": "$$\n\\frac{1}{T}\\sum_t x^t_n\\ge\\phi_n,\\quad\\forall n\\in\\mathcal N,\\qquad\\text{var. }x^t_n,y^t_n,z^t\\in\\{0,1\\},\\ \\alpha^t_{n,m},\\beta^t_m\\in[0,1],\\quad\\forall n\\in\\mathcal N,\\ \\forall m\\in\\mathcal M^t,\\ \\forall t\\in\\mathcal T. \\tag{1g}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec2-012",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"sec2-012"
],
"translation_ids": [
"zh-sec2-012"
],
"source": "The objective (1) minimizes the social cost. Constraint (1a) ensures the minimum number of models for ensemble learning. Constraint (1b) enforces the purchase budget. Constraint (1c) normalizes the weights, without loss of generality. Constraint (1d) and (1e) ensure that the weight can be non-zero only if the corresponding model is hosted. Constraint (1f) ensures that a model can be hosted only if the corresponding bid wins in the auction. Constraint (1g) ensures the long-term participation. The domains for the decision variables are specified finally.",
"translation": "目标函数 (1) 最小化社会成本。约束 (1a) 保证用于集成学习的最少模型数。约束 (1b) 施加购买预算。约束 (1c) 对权重做归一化，且不失一般性。约束 (1d) 与 (1e) 保证：只有当对应模型被托管时，其权重才可能非零。约束 (1f) 保证：只有当对应投标在拍卖中获胜时，该模型才可能被托管。约束 (1g) 保证长期参与。最后给出了决策变量的取值范围。",
"notes": {
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"origin": "source"
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},
{
"id": "note-sec2-04",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"note-sec2-04"
],
"translation_ids": [
"zh-note-sec2-04"
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"source": "",
"translation": "**七条约束各自锁住了什么（便于复现）。** (1a) 最低托管数 $\\ge W$：保证集成至少由 $W$ 个模型组成。
(1b) 购买数 $\\le Q^t$：预算约束，与 (1a) 一起构成“背包”结构。
(1c) 权重和为 1：避免权重整体缩放带来的退化（否则把所有权重同乘 2 也能降低损失）。
(1d)(1e) 权重与托管状态的一致性：$\\alpha^t_{n,m}\\le y^t_n$、$\\beta^t_m\\le z^t$——没托管的模型权重必须为 0。
(1f) $x^t_n\\ge y^t_n$：托管必须先中标，不能“白用”未购买的模型。
(1g) 长期参与：$\\frac1T\\sum_t x^t_n\\ge\\phi_n$，是一条跨期约束，不能逐期满足——这是算法 1 必须把约束吸进目标的原因。",
"notes": {
"kind": "blue",
"origin": "source"
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},
{
"id": "sec2-013",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"sec2-013"
],
"translation_ids": [
"zh-sec2-013"
],
"source": "**Algorithmic Challenges:** Solving the problem $\\mathcal{P}_0$ online is non-trivial due to multiple fundamental challenges. First, the switching cost term $\\sum_t\\sum_n\\Delta^t_n u^t_n[y^t_n-y^{t-1}_n]^+$ couples every time slot $t-1$ and its next time slot $t$. At $t-1$, as we have no idea whether we will want to host the model at $t$, it is difficult to decide $y^{t-1}_n$ to optimize the switching cost between $t-1$ and $t$. Second, the long-term constraint of participation $\\sum_t x^t_n\\ge\\sum_t\\phi_n$ needs to be considered carefully. Determining $x^t_n$ at the current time slot $t$ affects not only the cost at $t$ but also the determination of $x^t_n$ for future $t$, in order to satisfy this constraint. Third, our problem is nonlinear and NP-hard. If we ignore all the terms related to $x$, $z$, $\\alpha$, $\\beta$ and the switching cost, our problem could then become the minimum-cost knapsack problem, which is known to be NP-hard. Solving an NP-hard problem on the fly as the inputs gradually reveal themselves can be more challenging. Fourth, we need to decide each winner's payment to satisfy the economic properties of truthfulness and individual rationality, as it is intertwined with the previous three challenges.",
"translation": "**算法挑战：** 在线求解问题 $\\mathcal{P}_0$ 并不简单，存在若干根本性挑战。第一，切换成本项 $\\sum_t\\sum_n\\Delta^t_n u^t_n[y^t_n-y^{t-1}_n]^+$ 把每个时隙 $t-1$ 与其后一时隙 $t$ **耦合**在一起。在 $t-1$ 时刻，我们并不知道在 $t$ 是否还想要托管该模型，因此难以决定 $y^{t-1}_n$ 来优化 $t-1$ 与 $t$ 之间的切换成本。第二，参与约束 $\\sum_t x^t_n\\ge\\sum_t\\phi_n$ 这一**长期**约束需要仔细处理：在当前时隙 $t$ 决定 $x^t_n$，不仅影响 $t$ 时刻的成本，还会影响未来各 $t$ 的 $x^t_n$ 取值，因为要满足该约束。第三，我们的问题是非线性且 NP 难的：若忽略所有与 $x$、$z$、$\\alpha$、$\\beta$ 相关的项以及切换成本，问题就退化为最小成本背包问题，而已知它是 NP 难的；而在输入逐步显现的过程中“即时”求解一个 NP 难问题会更加困难。第四，我们还需要决定每个获胜者的支付，以满足真实性与个体理性这两项经济性质，而这件事与前三个挑战相互交织。",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "sec2-014",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"sec2-014"
],
"translation_ids": [
"zh-sec2-014"
],
"source": "**Algorithms Roadmap:** Our mechanism design incorporates a set of polynomial-time online algorithms to overcome the aforementioned challenges, as shown in Fig. 4. Section III describes our Algorithms 1, 2, and 3. Algorithm 1 outputs the fractional bid-selection decisions while accommodating the long-term constraint, and Algorithm 2 converts such fractional decisions into integers. Algorithm 3 further determines the payment for each bid. In this section, we define and prove the dynamic regret and the dynamic fitness with Algorithms 1 and 2, and also define and prove the truthfulness and the individual rationality with Algorithm 3. Section IV describes our Algorithms 4 and 5. Algorithm 4 makes dynamic trade-offs between switching to a new decision and keeping the previous decision regarding model hosting, while actually invoking Algorithms 1 and 2 for bid selections. Algorithm 5 updates the weights for all the deployed models while conducting ensemble learning upon the data stream. In this section, we prove the competitive ratio of our entire approach, and also prove the loss bound of ensemble learning.",
"translation": "**算法路线图：** 我们的机制设计包含一组多项式时间的在线算法，用以克服上述挑战，如图 4 所示。第三节介绍算法 1、2、3：算法 1 在兼顾长期约束的同时输出分数式投标选择决策，算法 2 把这类分数决策转换为整数，算法 3 进一步确定对每份投标的支付；本节我们定义并证明算法 1 与 2 的动态遗憾与动态拟合，并定义与证明算法 3 的真实性与个体理性。第四节介绍算法 4 与 5：算法 4 在“切换到新决策”与“保持先前决策”之间就模型托管做动态权衡，并实际调用算法 1 与 2 完成投标选择；算法 5 在对数据流开展集成学习的同时更新所有已部署模型的权重；该节我们证明整个方法的竞争比，并证明集成学习的损失界。",
"notes": {
"kind": null,
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},
{
"id": "table-mechanism",
"type": "table",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"table-mechanism"
],
"translation_ids": [
"zh-table-mechanism"
],
"source": "**Our Mechanism**\n\n| Loop / stage | Action |\n|---|---|\n| `for t = 1 to T do` | — |\n| ▷ Model Hosting and Winning-Bid Selection | Invoke Algorithm 4 to purchase and host models, which invokes Algorithm 1 and Algorithm 2 |\n| ▷ Ensemble Learning | Invoke Algorithm 5 to obtain weights for the models and conduct inference upon the data stream |\n| ▷ Payment Allocation | Invoke Algorithm 3 to calculate payments to the bids |",
"translation": "**我们的机制**\n\n| 循环 / 阶段 | 动作 |\n|---|---|\n| `for t = 1 to T do` | — |\n| ▷ 模型托管与获胜投标选择 | 调用算法 4 购买并托管模型，其中又调用算法 1 与算法 2 |\n| ▷ 集成学习 | 调用算法 5 获得各模型的权重，并对数据流执行推理 |\n| ▷ 支付分配 | 调用算法 3 计算对各投标的支付 |",
"notes": {
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},
{
"id": "note-sec2-05",
"type": "paragraph",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"note-sec2-05"
],
"translation_ids": [
"zh-note-sec2-05"
],
"source": "",
"translation": "**这个“Our Mechanism”框是全文的主循环。** 它把第 III、IV 节的五个算法串成一个每时隙执行的流程：先托管与选标（算法 4 → 1、2），再集成推理（算法 5），最后付钱（算法 3）。注意支付放在最后：因为定价要用到“实际决策”，而实际决策要等算法 1、2 算完。",
"notes": {
"kind": "green",
"origin": "source"
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},
{
"id": "fig-2-caption",
"type": "caption",
"section": "第二节 模型与问题形式化",
"source_page": 3,
"source_ids": [
"fig-2-caption"
],
"translation_ids": [
"zh-fig-2-caption"
],
"source": "Fig. 2. System workflow in a single time slot.",
"translation": "图 2 单个时隙内的系统工作流。",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "fig-3-caption",
"type": "caption",
"section": "第二节 模型与问题形式化",
"source_page": 4,
"source_ids": [
"fig-3-caption"
],
"translation_ids": [
"zh-fig-3-caption"
],
"source": "Fig. 3. Ensemble learning for a single data sample.",
"translation": "图 3 针对单个数据样本的集成学习。",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "fig-4-caption",
"type": "caption",
"section": "第二节 模型与问题形式化",
"source_page": 5,
"source_ids": [
"fig-4-caption"
],
"translation_ids": [
"zh-fig-4-caption"
],
"source": "Fig. 4. Structure of our proposed approach.",
"translation": "图 4 本文所提方法的结构。",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "sec3-heading",
"type": "heading",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"sec3-heading"
],
"translation_ids": [
"zh-sec3-heading"
],
"source": "III. BID SELECTION AND PAYMENT ALLOCATION",
"translation": "第三节 投标选择与支付分配",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "sec3-sub-a",
"type": "heading",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"sec3-sub-a"
],
"translation_ids": [
"zh-sec3-sub-a"
],
"source": "A. Algorithm 1: Selecting Fractional Bids",
"translation": "A. 算法 1：选择分数式投标",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "sec3-001",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"sec3-001"
],
"translation_ids": [
"zh-sec3-001"
],
"source": "We note that if $y^t$ is given (which will be further described in Section IV-A), then we can actually extract the following problem $\\mathcal{P}_1$ from the original problem $\\mathcal{P}_0$:",
"translation": "我们注意到，若 $y^t$ 已给定（其确定方式见第四节 A），那么就可以从原问题 $\\mathcal{P}_0$ 中提取出如下问题 $\\mathcal{P}_1$：",
"notes": {
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},
{
"id": "eq-002",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-002"
],
"translation_ids": [
"zh-eq-002"
],
"source": "$$\n\\mathcal P_1:\\min\\sum_t\\sum_n x^t_n c^t_n, \\tag{2}\n$$",
"translation": "$$\n\\mathcal P_1:\\min\\sum_t\\sum_n x^t_n c^t_n, \\tag{2}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-002a",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-002a"
],
"translation_ids": [
"zh-eq-002a"
],
"source": "$$\n\\text{s.t. }x^t_n\\ge y^t_n,\\quad\\forall n\\in\\mathcal N,\\ t\\in\\mathcal T, \\tag{2a}\n$$",
"translation": "$$\n\\text{s.t. }x^t_n\\ge y^t_n,\\quad\\forall n\\in\\mathcal N,\\ t\\in\\mathcal T, \\tag{2a}\n$$",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "eq-002b",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-002b"
],
"translation_ids": [
"zh-eq-002b"
],
"source": "$$\n\\sum_n x^t_n\\le Q^t,\\quad\\forall t\\in\\mathcal T, \\tag{2b}\n$$",
"translation": "$$\n\\sum_n x^t_n\\le Q^t,\\quad\\forall t\\in\\mathcal T, \\tag{2b}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-002c",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-002c"
],
"translation_ids": [
"zh-eq-002c"
],
"source": "$$\n\\frac{1}{T}\\sum_t x^t_n\\ge\\phi_n,\\quad\\forall n\\in\\mathcal N,\\qquad\\text{var. }x^t_n\\in\\{0,1\\},\\ \\forall n\\in\\mathcal N,\\ \\forall t\\in\\mathcal T. \\tag{2c}\n$$",
"translation": "$$\n\\frac{1}{T}\\sum_t x^t_n\\ge\\phi_n,\\quad\\forall n\\in\\mathcal N,\\qquad\\text{var. }x^t_n\\in\\{0,1\\},\\ \\forall n\\in\\mathcal N,\\ \\forall t\\in\\mathcal T. \\tag{2c}\n$$",
"notes": {
"kind": null,
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},
{
"id": "sec3-002",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"sec3-002"
],
"translation_ids": [
"zh-sec3-002"
],
"source": "For a concise presentation, we denote the objective function of $\\mathcal{P}_1$ as $f^t(x^t)=\\sum_n x^t_n c^t_n$. We also denote $g^t_n=\\phi_n-x^t_n,\\ \\forall n\\in\\mathcal{N}$; $g^t(x^t)=[g^t_1,\\dots,g^t_N]$; $h^t_n=x^t_n-y^t_n,\\ \\forall n\\in\\mathcal{N}$; $h^t(x^t)=[h^t_1,\\dots,h^t_N]$; and $d^t(x^t)=\\sum_n x^t_n-Q^t$. We can further relax the bid-selection control variables to the real domain, and thus transform $\\mathcal{P}_1$ to a linear program. That is,",
"translation": "为表述简洁，我们把 $\\mathcal{P}_1$ 的目标函数记为 $f^t(x^t)=\\sum_n x^t_n c^t_n$。我们另记 $g^t_n=\\phi_n-x^t_n,\\ \\forall n\\in\\mathcal{N}$；$g^t(x^t)=[g^t_1,\\dots,g^t_N]$；$h^t_n=x^t_n-y^t_n,\\ \\forall n\\in\\mathcal{N}$；$h^t(x^t)=[h^t_1,\\dots,h^t_N]$；以及 $d^t(x^t)=\\sum_n x^t_n-Q^t$。进一步地，我们可以把投标选择的控制变量松弛到实数域，从而把 $\\mathcal{P}_1$ 转化为一个线性规划，即",
"notes": {
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},
{
"id": "eq-003",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-003"
],
"translation_ids": [
"zh-eq-003"
],
"source": "$$\n\\mathcal P_2:\\min\\sum_t f^t(x^t), \\tag{3}\n$$",
"translation": "$$\n\\mathcal P_2:\\min\\sum_t f^t(x^t), \\tag{3}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-003a",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-003a"
],
"translation_ids": [
"zh-eq-003a"
],
"source": "$$\n\\text{s.t. }h^t(x^t)\\succeq 0, \\tag{3a}\n$$",
"translation": "$$\n\\text{s.t. }h^t(x^t)\\succeq 0, \\tag{3a}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-003b",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-003b"
],
"translation_ids": [
"zh-eq-003b"
],
"source": "$$\nd^t(x^t)\\le 0, \\tag{3b}\n$$",
"translation": "$$\nd^t(x^t)\\le 0, \\tag{3b}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-003c",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-003c"
],
"translation_ids": [
"zh-eq-003c"
],
"source": "$$\n\\sum_t g^t(x^t)\\preceq 0,\\qquad\\text{var. }x^t\\in X=\\{x^t\\,|\\,x^t_n\\in[0,1],\\ \\forall n\\in\\mathcal N,\\ \\forall t\\in\\mathcal T\\}. \\tag{3c}\n$$",
"translation": "$$\n\\sum_t g^t(x^t)\\preceq 0,\\qquad\\text{var. }x^t\\in X=\\{x^t\\,|\\,x^t_n\\in[0,1],\\ \\forall n\\in\\mathcal N,\\ \\forall t\\in\\mathcal T\\}. \\tag{3c}\n$$",
"notes": {
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},
{
"id": "sec3-003",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"sec3-003"
],
"translation_ids": [
"zh-sec3-003"
],
"source": "Solving the above problem $\\mathcal{P}_2$ is equivalent to solving its min-max version as follows:",
"translation": "求解上述问题 $\\mathcal{P}_2$ 等价于求解其如下极小–极大（min-max）形式：",
"notes": {
"kind": null,
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},
{
"id": "eq-004",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-004"
],
"translation_ids": [
"zh-eq-004"
],
"source": "$$\n\\min_{x}\\max_{\\lambda}\\sum_t L^t(x^t,\\lambda^t)=\\sum_t f^t(x^t)+\\sum_t\\lambda^t g^t(x^t),\\qquad\\text{s.t. }h^t(x^t)\\succeq 0,\\ d^t(x^t)\\le 0,\\ x^t\\in X, \\tag{4}\n$$",
"translation": "$$\n\\min_{x}\\max_{\\lambda}\\sum_t L^t(x^t,\\lambda^t)=\\sum_t f^t(x^t)+\\sum_t\\lambda^t g^t(x^t),\\qquad\\text{s.t. }h^t(x^t)\\succeq 0,\\ d^t(x^t)\\le 0,\\ x^t\\in X, \\tag{4}\n$$",
"notes": {
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},
{
"id": "sec3-004",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"sec3-004"
],
"translation_ids": [
"zh-sec3-004"
],
"source": "where $\\lambda^t$ is the Lagrange multiplier at $t$, and the long-term constraint (3c) has been absorbed into the objective so that we do not have to worry about it at this point. Based on (4), we can now solve $\\mathcal{P}_2$ on the fly at each $t+1$ by a standard dual ascent step to update the dual variable $\\lambda^{t+1}$ as in (5), and a modified descent step to minimize $L^t(x,\\lambda^{t+1})$ and obtain the fractional solution $\\tilde{x}^{t+1}$ as in (6).",
"translation": "其中 $\\lambda^t$ 是 $t$ 时刻的拉格朗日乘子，而长期约束 (3c) 已被吸收进目标函数，因此在此阶段无须再单独处理它。基于 (4)，我们现在可以在每个 $t+1$ 时刻即时求解 $\\mathcal{P}_2$：先用标准的对偶上升步按式 (5) 更新对偶变量 $\\lambda^{t+1}$，再用一个修正的下降步最小化 $L^t(x,\\lambda^{t+1})$，并按式 (6) 得到分数解 $\\tilde{x}^{t+1}$。",
"notes": {
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"origin": "source"
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},
{
"id": "eq-005",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-005"
],
"translation_ids": [
"zh-eq-005"
],
"source": "$$\n\\lambda^{t+1}=\\left[\\lambda^t+\\eta\\nabla_{\\lambda}L^t(\\tilde{x}^t,\\lambda^t)\\right]^+, \\tag{5}\n$$",
"translation": "$$\n\\lambda^{t+1}=\\left[\\lambda^t+\\eta\\nabla_{\\lambda}L^t(\\tilde{x}^t,\\lambda^t)\\right]^+, \\tag{5}\n$$",
"notes": {
"kind": null,
"origin": "source"
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"id": "sec3-005",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
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],
"translation_ids": [
"zh-sec3-005"
],
"source": "where $\\eta>0$ is the step size; $\\nabla_{\\lambda}L^t(\\tilde{x}^t,\\lambda^t)$ is the gradient of $L^t(\\tilde{x}^t,\\lambda)$ given $\\lambda=\\lambda^t$; and $\\tilde{x}^t$ is the fractional solution previously solved at $t$.",
"translation": "其中 $\\eta>0$ 是步长；$\\nabla_{\\lambda}L^t(\\tilde{x}^t,\\lambda^t)$ 是在 $\\lambda=\\lambda^t$ 处 $L^t(\\tilde{x}^t,\\lambda)$ 的梯度；$\\tilde{x}^t$ 是在 $t$ 时刻此前求得的分数解。",
"notes": {
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"origin": "source"
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},
{
"id": "eq-006",
"type": "equation",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"eq-006"
],
"translation_ids": [
"zh-eq-006"
],
"source": "$$\n\\min\\nabla f^t(\\tilde{x}^t)(x-\\tilde{x}^t)+\\lambda^{t+1}g^t(x)+\\frac{1}{2\\gamma}\\|x-\\tilde{x}^t\\|^2,\\qquad\\text{s.t. }h^t(x)\\succeq 0,\\ d^t(x)\\le 0,\\ x\\in X, \\tag{6}\n$$",
"translation": "$$\n\\min\\nabla f^t(\\tilde{x}^t)(x-\\tilde{x}^t)+\\lambda^{t+1}g^t(x)+\\frac{1}{2\\gamma}\\|x-\\tilde{x}^t\\|^2,\\qquad\\text{s.t. }h^t(x)\\succeq 0,\\ d^t(x)\\le 0,\\ x\\in X, \\tag{6}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-006",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"sec3-006"
],
"translation_ids": [
"zh-sec3-006"
],
"source": "where $\\gamma$ is a predefined constant and $\\nabla f^t(\\tilde{x}^t)$ is the gradient of $f^t(x)$ at $x=\\tilde{x}^t$. This can be called a Modified Online Saddle-Point (MOSP) method [38]. MOSP differs from Online Mirror Descent (OMD), since standard OMD does not involve primal-dual updates [52], [53], but primal-dual-related OMD and its variants do not often capture either the constraint violation or the long-term time-varying constraints [54], [55], [56], [57], [58], [59], [60]. MOSP also relates to constrained online learning, as the latter focuses on the long-term time-invariant constraints [61], [62], [63], [64] or the static regret [65], [66], [67], [68]. Algorithm 1 follows exactly the above idea. Through such alternate descent-ascent steps, we solve for $x^{t+1}$ and $\\lambda^{t+1}$ at each $t+1$ using only the inputs that have been known before $t+1$ rather than the unknowable future information beyond (and including) $t+1$. $L^t(x,\\lambda^{t+1})$ is approximated by $\\nabla f^t(\\tilde{x}^t)(x-\\tilde{x}^t)+\\lambda^{t+1}g^t(x)$, and $\\frac{1}{2\\gamma}\\|x-\\tilde{x}^t\\|^2$ is a regularization and proximal term. The problem (6) is solvable using standard convex optimization solvers which can find the $\\nu$-accurate optimal solution in $O(N^2\\log(1/\\nu))$ time [69] via the interior-point method, for example.",
"translation": "其中 $\\gamma$ 是预设常数，$\\nabla f^t(\\tilde{x}^t)$ 是 $f^t(x)$ 在 $x=\\tilde{x}^t$ 处的梯度。这可以称为修正在线鞍点（MOSP）方法 [38]。MOSP 与在线镜像下降（OMD）不同：标准 OMD 不含原始–对偶更新 [52], [53]，而与原始–对偶相关的 OMD 及其变体往往既无法刻画约束违反量，也无法处理长期的时变约束 [54], [55], [56], [57], [58], [59], [60]。MOSP 也与受约束在线学习相关，但后者关注的是长期时不变约束 [61], [62], [63], [64] 或静态遗憾 [65], [66], [67], [68]。算法 1 正是按上述思路工作的。通过这种交替的下降–上升步骤，我们在每个 $t+1$ 求解 $x^{t+1}$ 与 $\\lambda^{t+1}$ 时，只使用 $t+1$ 之前已知的输入，而不使用 $t+1$（含）之后不可知的未来信息。$L^t(x,\\lambda^{t+1})$ 由 $\\nabla f^t(\\tilde{x}^t)(x-\\tilde{x}^t)+\\lambda^{t+1}g^t(x)$ 近似，而 $\\frac{1}{2\\gamma}\\|x-\\tilde{x}^t\\|^2$ 是正则化与近似项。问题 (6) 可用标准凸优化求解器求解，例如通过内点法在 $O(N^2\\log(1/\\nu))$ 时间内找到 $\\nu$-精确最优解 [69]。",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "note-sec3-01",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"note-sec3-01"
],
"translation_ids": [
"zh-note-sec3-01"
],
"source": "",
"translation": "**从 $\\mathcal{P}_0$ 到式 (6)：把一条跨期约束“吸”进目标函数的三步。**
**① 分解（$\\mathcal{P}_0\\to\\mathcal{P}_1$）**：把与 $y$、$z$、$\\alpha$、$\\beta$、损失相关的项暂时剥离，只留 $\\sum_t\\sum_n x^t_nc^t_n$，并把 (1a)–(1f) 中与 $x$ 有关的约束（(1b)、(1f)、(1g)）留下，这就是 (2)(2a)–(2c)。
**② 松弛（$\\mathcal{P}_1\\to\\mathcal{P}_2$）**：把 $x^t_n\\in\\{0,1\\}$ 松弛为 $[0,1]$，问题变成线性规划 (3)。这一步故意允许“买 0.7 份”，为后面的随机舍入留出空间。
**③ 拉格朗日化（$\\mathcal{P}_2\\to$ (4)）**：把长期约束 (3c) 用乘子 $\\lambda^t$ 搬进目标，于是只需交替更新 $x$（下降）与 $\\lambda$（上升）。
为什么这么绕：因为 (3c) 是跨 T 期的，任何逐期贪婪都无法保证它；而把乘子也当作在线变量一起更新，就能在只看历史信息的前提下逐步逼近可行。代价是 (3c) 只被渐近满足——这正是后文要用“动态拟合”来量化其违反量的原因。",
"notes": {
"kind": "blue",
"origin": "source"
}
},
{
"id": "alg-1",
"type": "pseudocode",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"alg-1"
],
"translation_ids": [
"zh-alg-1"
],
"source": "Algorithm 1 Online Fractional Algorithm\n\nInput : Fractional solution x~^t, dual solution lambda^t, and y^t\nOutput: Fractional solution x~^(t+1)\n\n1 Initial: lambda^1 = 0, eta > 0\n2 Calculate lambda^(t+1) based on (5);\n3 Calculate x~^(t+1) by solving the problem (6) optimally;",
"translation": "算法 1 在线分数算法\n\n输入：分数解 x~^t、对偶解 lambda^t、以及 y^t\n输出：分数解 x~^(t+1)\n\n1 初始化：lambda^1 = 0，eta > 0\n2 依式 (5) 计算 lambda^(t+1)；\n3 通过最优求解问题 (6) 计算 x~^(t+1)；",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "sec3-sub-b",
"type": "heading",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"sec3-sub-b"
],
"translation_ids": [
"zh-sec3-sub-b"
],
"source": "B. Algorithm 2: Converting Fractional Bids to Integral Bids",
"translation": "B. 算法 2：把分数式投标转换为整数投标",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-007",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"sec3-007"
],
"translation_ids": [
"zh-sec3-007"
],
"source": "Algorithm 2 converts the fractional bid-selection decisions from Algorithm 1 into integers through a randomized rounding process without violating the constraints (2a) and (2b) during rounding while ensuring the expectation of each integer after rounding equals the corresponding fraction before rounding. Such expectation preservation is important for Algorithm 3.",
"translation": "算法 2 通过随机舍入过程，把算法 1 得到的分数式投标选择决策转换为整数，且在舍入过程中不违反约束 (2a) 与 (2b)，同时保证舍入后每个整数的期望等于舍入前对应的分数值。这种期望保持对算法 3 至关重要。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "alg-2",
"type": "pseudocode",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"alg-2"
],
"translation_ids": [
"zh-alg-2"
],
"source": "Algorithm 2 Randomized Rounding Algorithm\n\nInput : Fractions [x~^t_1, ..., x~^t_N]\nOutput: Integers [x_bar^t_1, ..., x_bar^t_N]\n\n 1 > Fractions scaling\n 2 Denote W~^t = [x~^t_1, ..., x~^t_N], eps = 1^T W~^t;\n 3 omega_1 = ceil(eps)/eps, omega_2 = floor(eps)/eps;\n 4 X~'^t = [omega_1 * x~^t_1, ..., omega_1 * x~^t_N] with probability eps - floor(eps)\n [omega_2 * x~^t_1, ..., omega_2 * x~^t_N] with probability ceil(eps) - eps\n 5 Define N' = N \\ {n | x~'^t_n in {0,1}};\n 6 > Fractions rounding\n 7 while N' != empty do\n 8 Select n_1, n_2 in N', n_1 != n_2;\n 9 phi_1 = min{1 - x~'^t_{n_1}, x~'^t_{n_2}}, phi_2 = min{1 - x~'^t_{n_2}, x~'^t_{n_1}};\n10 (x~''^t_{n_1}, x~''^t_{n_2}) = (x~'^t_{n_1} + phi_1, x~'^t_{n_2} - phi_1) with probability phi_2/(phi_1+phi_2)\n (x~'^t_{n_1} - phi_2, x~'^t_{n_2} + phi_2) with probability phi_1/(phi_1+phi_2)\n11 if x~''^t_{n_1} in {0,1} then x_bar^t_{n_1} = x~''^t_{n_1}, N' = N' \\ {n_1};\n12 else set x~'^t_{n_1} = x~''^t_{n_1};\n13 if x~''^t_{n_2} in {0,1} then x_bar^t_{n_2} = x~''^t_{n_2}, N' = N' \\ {n_2};\n14 else set x~'^t_{n_2} = x~''^t_{n_2};",
"translation": "算法 2 随机舍入算法\n\n输入：分数 [x~^t_1, ..., x~^t_N]\n输出：整数 [x_bar^t_1, ..., x_bar^t_N]\n\n 1 ▷ 分数缩放\n 2 记 W~^t = [x~^t_1, ..., x~^t_N]，eps = 1^T W~^t；\n 3 omega_1 = ceil(eps)/eps，omega_2 = floor(eps)/eps；\n 4 X~'^t = [omega_1 * x~^t_1, ..., omega_1 * x~^t_N] 以概率 eps - floor(eps)\n [omega_2 * x~^t_1, ..., omega_2 * x~^t_N] 以概率 ceil(eps) - eps\n 5 定义 N' = N \\ {n | x~'^t_n ∈ {0,1}}；\n 6 ▷ 分数舍入\n 7 while N' != 空 do\n 8 选取 n_1, n_2 ∈ N'，n_1 != n_2；\n 9 phi_1 = min{1 - x~'^t_{n_1}, x~'^t_{n_2}}，phi_2 = min{1 - x~'^t_{n_2}, x~'^t_{n_1}}；\n10 (x~''^t_{n_1}, x~''^t_{n_2}) = (x~'^t_{n_1} + phi_1, x~'^t_{n_2} - phi_1) 以概率 phi_2/(phi_1+phi_2)\n (x~'^t_{n_1} - phi_2, x~'^t_{n_2} + phi_2) 以概率 phi_1/(phi_1+phi_2)\n11 if x~''^t_{n_1} ∈ {0,1} then x_bar^t_{n_1} = x~''^t_{n_1}，N' = N' \\ {n_1}；\n12 else 置 x~'^t_{n_1} = x~''^t_{n_1}；\n13 if x~''^t_{n_2} ∈ {0,1} then x_bar^t_{n_2} = x~''^t_{n_2}，N' = N' \\ {n_2}；\n14 else 置 x~'^t_{n_2} = x~''^t_{n_2}；",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec3-02",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 5,
"source_ids": [
"note-sec3-02"
],
"translation_ids": [
"zh-note-sec3-02"
],
"source": "",
"translation": "**第 10 行的两个概率是怎么定出来的（原文未给推导，这里补上）。** 记 $p$ 为取第一支 $(+\\phi_1,-\\phi_1)$ 的概率，则
$\\mathbb{E}[\\tilde{x}''^t_{n_1}]=p(\\tilde{x}'^t_{n_1}+\\phi_1)+(1-p)(\\tilde{x}'^t_{n_1}-\\phi_2)=\\tilde{x}'^t_{n_1}+p\\phi_1-(1-p)\\phi_2$。
要保持期望不变，需 $p\\phi_1=(1-p)\\phi_2$，解得 $p=\\phi_2/(\\phi_1+\\phi_2)$。
因此第一支概率为 $\\phi_2/(\\phi_1+\\phi_2)$，第二支 $(-\\phi_2,+\\phi_2)$ 为 $\\phi_1/(\\phi_1+\\phi_2)$。我按这一推导填写伪代码：原文该处因两列排版导致分子分母错位，抽取文本中两个概率都读作 $\\phi_1/(\\phi_1+\\phi_2)$，与“期望保持”矛盾，不能照录；此处属据数学约束反推，已在数学复核中标注。",
"notes": {
"kind": "blue",
"origin": "source"
}
},
{
"id": "sec3-008",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-008"
],
"translation_ids": [
"zh-sec3-008"
],
"source": "Fractions scaling as in Lines 2~5 adjusts the fractions and ensures that the sum of the fractions after adjusting equals an integer. In Line 4, after adjusting, each column of $\\tilde{W}^t$ either increases by multiplying $\\omega_1>1$ or decreases by multiplying $\\omega_2<1$. Thus, we have $\\mathbb{E}[\\tilde{X}'^t]=\\frac{\\lceil\\epsilon\\rceil}{\\epsilon}\\tilde{W}^t\\cdot(\\epsilon-\\lfloor\\epsilon\\rfloor)+\\frac{\\lfloor\\epsilon\\rfloor}{\\epsilon}\\tilde{W}^t\\cdot(\\lceil\\epsilon\\rceil-\\epsilon)=(\\lceil\\epsilon\\rceil-\\lfloor\\epsilon\\rfloor)\\tilde{W}^t=\\tilde{W}^t$. We should mention that the sum of $\\tilde{x}^t_n$ increases to at most $\\lceil\\epsilon\\rceil$, and $Q^t$ is an integer, so (2b) still holds after adjusting; and (2a) always holds.",
"translation": "第 2∼5 行的分数缩放会调整分数，并保证调整后各分数之和为整数。在第 4 行，调整后 $\\tilde{W}^t$ 的每一列要么乘以 $\\omega_1>1$ 而增大，要么乘以 $\\omega_2<1$ 而减小。于是有 $\\mathbb{E}[\\tilde{X}'^t]=\\frac{\\lceil\\epsilon\\rceil}{\\epsilon}\\tilde{W}^t\\cdot(\\epsilon-\\lfloor\\epsilon\\rfloor)+\\frac{\\lfloor\\epsilon\\rfloor}{\\epsilon}\\tilde{W}^t\\cdot(\\lceil\\epsilon\\rceil-\\epsilon)=(\\lceil\\epsilon\\rceil-\\lfloor\\epsilon\\rfloor)\\tilde{W}^t=\\tilde{W}^t$。需要指出，$\\tilde{x}^t_n$ 之和最多增大到 $\\lceil\\epsilon\\rceil$，而 $Q^t$ 是整数，因此调整后 (2b) 仍然成立；(2a) 则始终成立。",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "note-sec3-03",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"note-sec3-03"
],
"translation_ids": [
"zh-note-sec3-03"
],
"source": "",
"translation": "**这一步为什么“不会越界”（原文的推理细节）。** 缩放把 $\\sum_n\\tilde{x}^t_n=\\epsilon$ 抬到至多 $\\lceil\\epsilon\\rceil$。因为购买约束是 $\\sum_n x^t_n\\le Q^t$ 且 $Q^t$ 为整数，而缩放前有 $\\epsilon\\le Q^t$，于是 $\\lceil\\epsilon\\rceil\\le Q^t$（$\\epsilon\\le Q^t$ 且 $Q^t$ 为整数 $\\Rightarrow$ $\\lceil\\epsilon\\rceil\\le Q^t$）——所以 (2b) 不会被破坏。这是“先抬后舍”这一顺序的必要性：若先舍入再缩放，就可能越过 $Q^t$。",
"notes": {
"kind": "blue",
"origin": "source"
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},
{
"id": "sec3-009",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-009"
],
"translation_ids": [
"zh-sec3-009"
],
"source": "Fractions rounding as in Lines 7~14 iteratively selects a pair of fractions and converts at least one of them into an integer in each iteration. Since the sum of all columns is an integer beforehand due to the previous step, it can be guaranteed that $\\tilde{X}'^t$ as a vector only contains 0 and 1 after the loop. In Line 10, the sum is preserved, because $\\tilde{x}''^t_{n_1}+\\tilde{x}''^t_{n_2}=(\\tilde{x}'^t_{n_1}+\\phi_1)+(\\tilde{x}'^t_{n_2}-\\phi_1)=\\tilde{x}'^t_{n_1}+\\tilde{x}'^t_{n_2}$, for example. Also, the expectation is preserved. We note that Lines 9 and 10 guarantee that in each iteration of the loop at least one fraction will be rounded to either 0 or 1. This fractions rounding phase borrows the idea of dependent rounding [70]. The time complexity of Algorithm 2 is $O(N)$.",
"translation": "第 7∼14 行的分数舍入迭代地选取一对分数，并在每次迭代中把其中至少一个转换为整数。由于上一步之后所有列之和已是整数，因此可以保证循环结束后向量 $\\tilde{X}'^t$ 只含 0 与 1。第 10 行保持了总和，因为例如 $\\tilde{x}''^t_{n_1}+\\tilde{x}''^t_{n_2}=(\\tilde{x}'^t_{n_1}+\\phi_1)+(\\tilde{x}'^t_{n_2}-\\phi_1)=\\tilde{x}'^t_{n_1}+\\tilde{x}'^t_{n_2}$。同时，期望也被保持。我们注意到第 9 行与第 10 行保证：循环的每次迭代中至少有一个分数会被舍入为 0 或 1。该分数舍入阶段借鉴了相依舍入（dependent rounding）的思想 [70]。算法 2 的时间复杂度为 $O(N)$。",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "sec3-sub-c",
"type": "heading",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-sub-c"
],
"translation_ids": [
"zh-sec3-sub-c"
],
"source": "C. Algorithm 3: Allocating Payment",
"translation": "C. 算法 3：支付分配",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "sec3-010",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-010"
],
"translation_ids": [
"zh-sec3-010"
],
"source": "Algorithm 3 calculates the payments to the winning bids output by Algorithm 2. Following the sufficient and necessary conditions for a randomized auction to be both truthful and individually rational [71], which will be formally defined in Section III-E, we use Line 2 to calculate the payment to the winning bids. Our auction at each time slot $t$ has become a randomized auction due to Algorithm 2. We note that the fractional solution $\\tilde{x}^t_n$ can be considered as a function of $c^t_n$ and $c^t_{-n}$, where the former is the bidding price reported by the bid $n$ and the latter is what is reported by all the other bids, because the value of $\\tilde{x}^t_n$ is calculated by Algorithm 1 using $c^t_n$ and $c^t_{-n}$ as the inputs. In other words, Algorithm 1 can be considered as the mapping from $c^t_n$ and $c^t_{-n}$ to $\\tilde{x}^t_n$. In a function format, we can just write $\\tilde{x}^t_n(c^t_n,c^t_{-n})$.",
"translation": "算法 3 计算对算法 2 输出的获胜投标的支付。依据“随机拍卖同时满足真实性与个体理性”的充要条件 [71]（该条件将在第三节 E 中正式定义），我们用第 2 行计算对获胜投标的支付。由于算法 2，我们在每个时隙 $t$ 的拍卖已成为随机拍卖。我们注意到，分数解 $\\tilde{x}^t_n$ 可以视为 $c^t_n$ 与 $c^t_{-n}$ 的函数：前者是投标 $n$ 报告的竞价，后者是其他所有投标报告的竞价；因为 $\\tilde{x}^t_n$ 的值正是算法 1 以 $c^t_n$ 与 $c^t_{-n}$ 为输入计算得到的。换言之，算法 1 可视为从 $c^t_n$ 与 $c^t_{-n}$ 到 $\\tilde{x}^t_n$ 的映射。写成函数形式，即 $\\tilde{x}^t_n(c^t_n,c^t_{-n})$。",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "alg-3",
"type": "pseudocode",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"alg-3"
],
"translation_ids": [
"zh-alg-3"
],
"source": "Algorithm 3 Payment Allocation Algorithm\n\nInput : [x_bar^t_1, ..., x_bar^t_N]\nOutput: Payment p^t_n, for all n\n\n1 for n, where x_bar^t_n = 1 do\n2 Set p^t_n = c^t_n * x~^t_n(c^t_n, c^t_-n) + integral from c^t_n to chi^t_n of x~^t_n(c, c^t_-n) dc,\n where chi^t_n = x~^t_n / gamma + 2 * lambda^(t+1)_n;\n3 for n, where x_bar^t_n = 0 do\n4 Set p^t_n = 0;",
"translation": "算法 3 支付分配算法\n\n输入：[x_bar^t_1, ..., x_bar^t_N]\n输出：支付 p^t_n，对所有 n\n\n1 for n，其中 x_bar^t_n = 1 do\n2 置 p^t_n = c^t_n * x~^t_n(c^t_n, c^t_-n) + 从 c^t_n 到 chi^t_n 对 x~^t_n(c, c^t_-n) dc 的积分，\n 其中 chi^t_n = x~^t_n / gamma + 2 * lambda^(t+1)_n；\n3 for n，其中 x_bar^t_n = 0 do\n4 置 p^t_n = 0；",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-011",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-011"
],
"translation_ids": [
"zh-sec3-011"
],
"source": "In Line 2 of Algorithm 3, to calculate the integral, we need to vary the value of $c^t_n$, simply denoted as $c$ here, keep $c^t_{-n}$, and invoke Algorithm 1 to calculate the corresponding $\\tilde{x}^t_n$. The integration interval's upper limit $\\chi^t_n$ needs to be set to satisfy the requirements in Theorem 2 which will be stated later. Specifically, we need to find out the value of $\\chi^t_n$ for $n$ at $t$, such that $\\int_0^{\\chi^t_n}\\tilde{x}^t_n(c,c^t_{-n})dc<\\infty$ and $\\int_{\\chi^t_n}^{\\infty}\\tilde{x}^t_n(c,c^t_{-n})dc=0$. Toward that end, we focus on the problem (6), whose objective function is as follows, where $x^{t+1}_n,\\forall n$ are the decision variables and $\\lambda^{t+1}_n,\\forall n$ come from (5): $\\sum_n(c^t_n(x^{t+1}_n-\\tilde{x}^t_n)+\\lambda^{t+1}_n(\\phi_n-2x^{t+1}_n+y^{t+1}_n)+\\frac{(x^{t+1}_n-\\tilde{x}^t_n)^2}{2\\gamma})$.",
"translation": "在算法 3 的第 2 行，为计算该积分，我们需要改变 $c^t_n$ 的取值（此处简记为 $c$），保持 $c^t_{-n}$ 不变，并调用算法 1 计算相应的 $\\tilde{x}^t_n$。积分区间的上限 $\\chi^t_n$ 的设置需满足后文定理 2 的要求。具体而言，我们需要找出 $t$ 时刻 $n$ 的 $\\chi^t_n$ 取值，使得 $\\int_0^{\\chi^t_n}\\tilde{x}^t_n(c,c^t_{-n})dc<\\infty$ 且 $\\int_{\\chi^t_n}^{\\infty}\\tilde{x}^t_n(c,c^t_{-n})dc=0$。为此，我们聚焦问题 (6)，其目标函数如下，其中 $x^{t+1}_n,\\forall n$ 是决策变量，而 $\\lambda^{t+1}_n,\\forall n$ 来自式 (5)：$\\sum_n(c^t_n(x^{t+1}_n-\\tilde{x}^t_n)+\\lambda^{t+1}_n(\\phi_n-2x^{t+1}_n+y^{t+1}_n)+\\frac{(x^{t+1}_n-\\tilde{x}^t_n)^2}{2\\gamma})$。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-012",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-012"
],
"translation_ids": [
"zh-sec3-012"
],
"source": "Note that this is a summation of a series of quadratic functions. For each $n$, we desire that, in the interval $[0,1]$, its optimal $x^{t+1}_n$ is 0. From the geometric image, we know that this can only be achieved when the vertical symmetry axis of the quadratic function falls on the non-positive half of the horizontal real axis. That is, we require $\\tilde{x}^t_n-\\gamma c^t_n+2\\gamma\\lambda^{t+1}_n\\le 0$, i.e., $c^t_n\\ge\\frac{\\tilde{x}^t_n}{\\gamma}+2\\lambda^{t+1}_n$. Then we conclude that $\\chi^t_n=\\frac{\\tilde{x}^t_n}{\\gamma}+2\\lambda^{t+1}_n$. The time complexity of Algorithm 3 is $O(N^3 i\\log(1/\\nu))$, where $i$ is the number of segments when dividing the range of $\\chi^t_n-c^t_n$ for calculating the integral numerically.",
"translation": "注意这是若干二次函数之和。对每个 $n$，我们希望其在区间 $[0,1]$ 上的最优 $x^{t+1}_n$ 为 0。从几何图像可知，只有当该二次函数的竖直对称轴落在水平实轴的非正半轴上时才可实现，即要求 $\\tilde{x}^t_n-\\gamma c^t_n+2\\gamma\\lambda^{t+1}_n\\le 0$，亦即 $c^t_n\\ge\\frac{\\tilde{x}^t_n}{\\gamma}+2\\lambda^{t+1}_n$。于是我们得出 $\\chi^t_n=\\frac{\\tilde{x}^t_n}{\\gamma}+2\\lambda^{t+1}_n$。算法 3 的时间复杂度为 $O(N^3 i\\log(1/\\nu))$，其中 $i$ 是数值计算积分时为划分 $\\chi^t_n-c^t_n$ 范围所取的段数。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec3-04",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"note-sec3-04"
],
"translation_ids": [
"zh-note-sec3-04"
],
"source": "",
"translation": "**$\\chi^t_n$ 的几何推导（原文一句话带过，这里展开）。** 把 (6) 中与单个 $n$ 有关的部分写成 $x=x^{t+1}_n$ 的二次函数：
$g(x)=c^t_n(x-\\tilde{x}^t_n)+\\lambda^{t+1}_n(\\phi_n-2x+y^{t+1}_n)+\\frac{(x-\\tilde{x}^t_n)^2}{2\\gamma}$。
二次项系数 $\\frac{1}{2\\gamma}>0$，故开口向上；对称轴在 $x^*=\\tilde{x}^t_n-\\gamma c^t_n+2\\gamma\\lambda^{t+1}_n$。
在 $[0,1]$ 上最优解为 $x=0$ 的充要条件是对称轴不超过 0，即 $x^*\\le0$ $\\Leftrightarrow$ $c^t_n\\ge\\frac{\\tilde{x}^t_n}{\\gamma}+2\\lambda^{t+1}_n$。
因此当 $c$ 增大到 $\\chi^t_n=\\frac{\\tilde{x}^t_n}{\\gamma}+2\\lambda^{t+1}_n$ 时 $\\tilde{x}^t_n(c,\\cdot)=0$，积分的尾部自然为零，这正是定理 2 条件 (ii) 所要求的。",
"notes": {
"kind": "blue",
"origin": "source"
}
},
{
"id": "sec3-sub-d",
"type": "heading",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-sub-d"
],
"translation_ids": [
"zh-sec3-sub-d"
],
"source": "D. Regret and Fit Analysis",
"translation": "D. 遗憾与拟合分析",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-013",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-013"
],
"translation_ids": [
"zh-sec3-013"
],
"source": "We define and adopt the dynamic regret and the dynamic fit as the performance metrics. We prove that the dynamic regret and the dynamic fit of our algorithms grow only sub-linearly along with the length of the entire time horizon.",
"translation": "我们定义并采用动态遗憾与动态拟合作为性能度量，并证明本算法的动态遗憾与动态拟合都只随整个时间视界的长度次线性增长。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-def-1",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-def-1"
],
"translation_ids": [
"zh-sec3-def-1"
],
"source": "**Definition 1 (Dynamic Regret and Dynamic Fit):** The dynamic regret and the dynamic fit for the problem $\\mathcal{P}_1$ are defined as follows, respectively: $\\mathrm{Reg}_T:=\\mathbb{E}[\\sum_{t=1}^{T}f^t(\\bar{x}^t)]-\\sum_{t=1}^{T}f^t(x^{t*})$, $\\mathrm{Fit}_T:=\\|[\\mathbb{E}[\\sum_{t=1}^{T}g^t(\\bar{x}^t)]]^+\\|$, where for each $t$, $\\bar{x}^t$ is the output of Algorithm 2 as described previously; $x^{t*}\\in\\arg\\min_{x^t\\in X^t}f^t(x^t)$; $X^t:=\\{x\\,|\\,h^t(x)\\succeq 0,d^t(x)\\le 0,g^t(x)\\preceq 0;x^t_n\\in\\{0,1\\},\\forall n\\}$.",
"translation": "**定义 1（动态遗憾与动态拟合）：** 问题 $\\mathcal{P}_1$ 的动态遗憾与动态拟合分别定义如下：$\\mathrm{Reg}_T:=\\mathbb{E}[\\sum_{t=1}^{T}f^t(\\bar{x}^t)]-\\sum_{t=1}^{T}f^t(x^{t*})$，$\\mathrm{Fit}_T:=\\|[\\mathbb{E}[\\sum_{t=1}^{T}g^t(\\bar{x}^t)]]^+\\|$，其中对每个 $t$，$\\bar{x}^t$ 是前述算法 2 的输出；$x^{t*}\\in\\arg\\min_{x^t\\in X^t}f^t(x^t)$；$X^t:=\\{x\\,|\\,h^t(x)\\succeq 0,d^t(x)\\le 0,g^t(x)\\preceq 0;x^t_n\\in\\{0,1\\},\\forall n\\}$。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-014",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-014"
],
"translation_ids": [
"zh-sec3-014"
],
"source": "While the dynamic regret captures the difference between the objective value incurred by our online solution and the sum of the optimal objective value at each time slot, the dynamic fit reflects the violation of Constraint (2c). Recall that (2c) was absorbed into the objective in Algorithm 1; so it is important to quantify the violation of this constraint. We actually have the following result:",
"translation": "动态遗憾刻画的是“在线解所付出的目标值”与“每个时隙最优目标值之和”之间的差距；而动态拟合反映的是约束 (2c) 的违反程度。回想一下，(2c) 在算法 1 中已被吸收进目标函数，因此量化该约束的违反量十分重要。我们实际上有如下结果：",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-thm-1",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-thm-1"
],
"translation_ids": [
"zh-sec3-thm-1"
],
"source": "**Theorem 1:** The dynamic regret and the dynamic fit satisfy $\\mathrm{Reg}_T\\le O(T^{\\frac{2}{3}})$ and $\\mathrm{Fit}_T\\le O(T^{\\frac{2}{3}})$. Proof: See Appendix A in our supplementary material. $\\square$",
"translation": "**定理 1：** 动态遗憾与动态拟合满足 $\\mathrm{Reg}_T\\le O(T^{\\frac{2}{3}})$ 与 $\\mathrm{Fit}_T\\le O(T^{\\frac{2}{3}})$。证明：见补充材料附录 A。$\\square$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-015",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-015"
],
"translation_ids": [
"zh-sec3-015"
],
"source": "Theorem 1 relies on some common assumptions, including the requirement that the variation in the environment is sub-linear, i.e., the cumulative variations of the per-time-slot minimizers and of the per-time-slot constraints grow sub-linearly with time, respectively. Note that the supplementary material is a separate document along with this paper.",
"translation": "定理 1 依赖若干常见假设，其中包括要求环境变化是次线性的，即各时隙最小点与各时隙约束的累计变化分别随时间次线性增长。注意补充材料是与本文配套的独立文档。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec3-05",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"note-sec3-05"
],
"translation_ids": [
"zh-note-sec3-05"
],
"source": "",
"translation": "**$O(T^{2/3})$ 意味着什么。** 它说的是累计遗憾的增长速度慢于时间本身：摊到每个时隙的平均遗憾是 $O(T^{2/3})/T=O(T^{-1/3})\\to0$。所以“时间平均的投标成本”会收敛到“时间平均的离线最优”。这正是原文“as the total number of time slots grows, the difference ... gradually vanishes”一句的确切含义。
注意：证明在补充材料（附录 A）里，本文正文未给出，且依赖“环境变化次线性”的假设。",
"notes": {
"kind": "green",
"origin": "source"
}
},
{
"id": "sec3-sub-e",
"type": "heading",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-sub-e"
],
"translation_ids": [
"zh-sec3-sub-e"
],
"source": "E. Economic Properties Analysis",
"translation": "E. 经济性质分析",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-016",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 6,
"source_ids": [
"sec3-016"
],
"translation_ids": [
"zh-sec3-016"
],
"source": "We define utility, based on which we further define truthfulness and individual rationality. We prove that our randomized auction mechanism satisfies both of these economic properties.",
"translation": "我们定义效用，并在此基础上进一步定义真实性与个体理性。我们证明所提出的随机拍卖机制同时满足这两项经济性质。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-def-2",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 7,
"source_ids": [
"sec3-def-2"
],
"translation_ids": [
"zh-sec3-def-2"
],
"source": "**Definition 2 (Utility):** The utility of the bid $n$ at time $t$ is $U^t_n(c^t_n,c^t_{-n})=p^t_n(\\hat{c}^t_n,\\hat{c}^t_{-n})-c^t_n\\mathbb{E}(\\bar{x}^t_n(\\hat{c}^t_n,\\hat{c}^t_{-n}))$ if $\\bar{x}^t_n=1$, and $0$ otherwise, where $\\hat{c}^t_n$ is the bidding price submitted by the bid $n$; $\\hat{c}^t_{-n}$ denotes the bidding prices of all the other bids except the bid $n$; and $c^t_n$ is the true cost of the bid $n$.",
"translation": "**定义 2（效用）：** 投标 $n$ 在时刻 $t$ 的效用为：当 $\\bar{x}^t_n=1$ 时 $U^t_n(c^t_n,c^t_{-n})=p^t_n(\\hat{c}^t_n,\\hat{c}^t_{-n})-c^t_n\\mathbb{E}(\\bar{x}^t_n(\\hat{c}^t_n,\\hat{c}^t_{-n}))$，否则为 $0$。其中 $\\hat{c}^t_n$ 是投标 $n$ 提交的竞价；$\\hat{c}^t_{-n}$ 表示除投标 $n$ 之外其他所有投标的竞价；$c^t_n$ 是投标 $n$ 的真实成本。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-def-3",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 7,
"source_ids": [
"sec3-def-3"
],
"translation_ids": [
"zh-sec3-def-3"
],
"source": "**Definition 3 (Truthfulness):** A randomized auction is truthful in expectation if every bid $n$ maximizes its expected utility by bidding its true cost, i.e., $U^t_n(c^t_n,\\hat{c}^t_{-n})\\ge U^t_n(\\hat{c}^t_n,\\hat{c}^t_{-n})$.",
"translation": "**定义 3（真实性）：** 若每个投标 $n$ 通过按真实成本报价即可使其期望效用最大，即 $U^t_n(c^t_n,\\hat{c}^t_{-n})\\ge U^t_n(\\hat{c}^t_n,\\hat{c}^t_{-n})$，则该随机拍卖是期望意义下真实的。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-def-4",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 7,
"source_ids": [
"sec3-def-4"
],
"translation_ids": [
"zh-sec3-def-4"
],
"source": "**Definition 4 (Individual Rationality):** A randomized auction is individually rational in expectation if every bid $n$ always achieves a non-negative utility, i.e., $U^t_n(\\hat{c}^t_n,\\hat{c}^t_{-n})\\ge 0$.",
"translation": "**定义 4（个体理性）：** 若每个投标 $n$ 总能获得非负效用，即 $U^t_n(\\hat{c}^t_n,\\hat{c}^t_{-n})\\ge 0$，则该随机拍卖是期望意义下个体理性的。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-thm-2",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 7,
"source_ids": [
"sec3-thm-2"
],
"translation_ids": [
"zh-sec3-thm-2"
],
"source": "**Theorem 2:** A randomized auction is truthful and individually rational in expectation if and only if the following conditions are met [71]: (i) $\\mathbb{E}(\\bar{x}^t_n)$ is monotonically non-increasing in $c^t_n,\\forall n$; (ii) $\\int_0^{\\infty}\\mathbb{E}(\\bar{x}^t_n)dc<\\infty,\\forall n$; (iii) the payment is in the form of $p^t_n=c^t_n\\mathbb{E}(\\bar{x}^t_n(c^t_n,c^t_{-n}))+\\int_{c^t_n}^{\\infty}\\mathbb{E}(\\bar{x}^t_n(c,c^t_{-n}))dc,\\forall n$. Our randomized auction mechanism satisfies these conditions. Proof: See Appendix B in our supplementary material. $\\square$",
"translation": "**定理 2：** 随机拍卖在期望意义下同时满足真实性与个体理性，当且仅当以下条件成立 [71]：(i) $\\mathbb{E}(\\bar{x}^t_n)$ 关于 $c^t_n$ 单调不增，$\\forall n$；(ii) $\\int_0^{\\infty}\\mathbb{E}(\\bar{x}^t_n)dc<\\infty,\\forall n$；(iii) 支付形如 $p^t_n=c^t_n\\mathbb{E}(\\bar{x}^t_n(c^t_n,c^t_{-n}))+\\int_{c^t_n}^{\\infty}\\mathbb{E}(\\bar{x}^t_n(c,c^t_{-n}))dc,\\forall n$。我们的随机拍卖机制满足这些条件。证明：见补充材料附录 B。$\\square$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec3-017",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 7,
"source_ids": [
"sec3-017"
],
"translation_ids": [
"zh-sec3-017"
],
"source": "The two economic properties are important because truthfulness encourages the bidder to report its true cost as the bidding price, and individual rationality guarantees no utility loss for the bidder regardless of the auction outcome. We note that Definitions 2~4 and Theorem 2 only deal with $\\mathbb{E}(\\bar{x}^t_n)$; yet, via Algorithms 1 and 2, we are able to establish $\\mathbb{E}(\\bar{x}^t_n)=\\tilde{x}^t_n$ and further prove that the conditions as required in Theorem 2 can be met by using $\\mathbb{E}(\\bar{x}^t_n)=\\tilde{x}^t_n$. Following Theorem 2, we can design Algorithm 3.",
"translation": "这两项经济性质之所以重要，是因为真实性促使竞标者按真实成本报价，而个体理性保证竞标者无论拍卖结果如何都不会蒙受效用损失。我们注意到，定义 2∼4 与定理 2 只涉及 $\\mathbb{E}(\\bar{x}^t_n)$；而通过算法 1 与算法 2，我们能够建立 $\\mathbb{E}(\\bar{x}^t_n)=\\tilde{x}^t_n$，并进一步证明：取 $\\mathbb{E}(\\bar{x}^t_n)=\\tilde{x}^t_n$ 即可满足定理 2 所要求的条件。依据定理 2，我们便能设计算法 3。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec3-06",
"type": "paragraph",
"section": "第三节 投标选择与支付分配",
"source_page": 7,
"source_ids": [
"note-sec3-06"
],
"translation_ids": [
"zh-note-sec3-06"
],
"source": "",
"translation": "**为什么随机舍入的“期望保持”是定理 2 能不能用的前提。** 定理 2 的三个条件是针对期望分配概率 $\\mathbb{E}(\\bar{x}^t_n)$ 陈述的，而算法 1 算出的是分数 $\\tilde{x}^t_n$。若舍入改变了期望（$\\mathbb{E}(\\bar{x}^t_n)\\ne\\tilde{x}^t_n$），我们就无法把 $\\tilde{x}^t_n$ 代进定理 2 的条件，上一节关于 $\\chi^t_n$ 的推导也就失效。所以算法 2 的“期望保持”不是装饰性性质，而是算法 3 合法性的前提。这也解释了原文为什么反复强调 expectation preservation。",
"notes": {
"kind": "green",
"origin": "source"
}
},
{
"id": "sec4-heading",
"type": "heading",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"sec4-heading"
],
"translation_ids": [
"zh-sec4-heading"
],
"source": "IV. MODEL HOSTING AND ENSEMBLE LEARNING",
"translation": "第四节 模型托管与集成学习",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec4-sub-a",
"type": "heading",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"sec4-sub-a"
],
"translation_ids": [
"zh-sec4-sub-a"
],
"source": "A. Algorithm 4: Hosting Models via Lazy Switch",
"translation": "A. 算法 4：通过懒惰切换托管模型",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec4-001",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"sec4-001"
],
"translation_ids": [
"zh-sec4-001"
],
"source": "Algorithm 4 neglects the inference loss tentatively and dynamically determines the changing set of the models to host at the service provider's facility as time goes. Our idea is to keep hosting the current set of models until the cumulative model hosting cost exceeds a pre-specified constant times the most recent switching cost of switching from a previous set of models to the current set of models. To determine the set of models that we would want to potentially switch to, we use $\\mathcal{P}^t_3$ at each $t$, which is extracted from our original problem $\\mathcal{P}_0$.",
"translation": "算法 4 暂时忽略推理损失，随时间动态确定在服务提供方设施处需要托管的模型集合。我们的思路是：持续托管当前这批模型，直到累计的模型托管成本超过“从上一批模型切换到当前这批模型的最新切换成本”的某个预设常数倍为止。为确定“可能想要切换过去”的模型集合，我们在每个 $t$ 使用从原问题 $\\mathcal{P}_0$ 中提取出的 $\\mathcal{P}^t_3$。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-007",
"type": "equation",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"eq-007"
],
"translation_ids": [
"zh-eq-007"
],
"source": "$$\n\\mathcal P^t_3:\\min\\sum_n y^t_n\\left(v^t_n+u^t_n(1-\\Delta^t_n)\\right)+e^t z^t, \\tag{7}\n$$",
"translation": "$$\n\\mathcal P^t_3:\\min\\sum_n y^t_n\\left(v^t_n+u^t_n(1-\\Delta^t_n)\\right)+e^t z^t, \\tag{7}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-007a",
"type": "equation",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"eq-007a"
],
"translation_ids": [
"zh-eq-007a"
],
"source": "$$\n\\text{s.t. }\\sum_n y^t_n\\le Q^t, \\tag{7a}\n$$",
"translation": "$$\n\\text{s.t. }\\sum_n y^t_n\\le Q^t, \\tag{7a}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "eq-007b",
"type": "equation",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"eq-007b"
],
"translation_ids": [
"zh-eq-007b"
],
"source": "$$\n\\sum_n y^t_n+z^t\\ge W,\\qquad\\text{var. }y^t_n,z^t\\in\\{0,1\\},\\ \\forall n\\in\\mathcal N. \\tag{7b}\n$$",
"translation": "$$\n\\sum_n y^t_n+z^t\\ge W,\\qquad\\text{var. }y^t_n,z^t\\in\\{0,1\\},\\ \\forall n\\in\\mathcal N. \\tag{7b}\n$$",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec4-002",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"sec4-002"
],
"translation_ids": [
"zh-sec4-002"
],
"source": "The coefficient matrix of the constraints of $\\mathcal{P}^t_3$ is totally unimodular [72]. Therefore, we can solve $\\mathcal{P}^t_3$ with its decision variables in $[0,1]$ via any standard linear program solver, and the optimal solution we obtain will be automatically in $\\{0,1\\}$. Algorithm 4 adopts the above idea in Line 6, where $k$ is the pre-specified parameter. We also define $C^t_{SC}(y^t,y^{t-1})=\\sum_n\\Delta^t_n u^t_n[y^t_n-y^{t-1}_n]^+$ and $C^t_{-SC}(x^t,y^t,z^t)=\\sum_n x^t_n c^t_n+\\sum_n y^t_n(v^t_n+u^t_n(1-\\Delta^t_n))+e^t z^t$. $\\hat{t}$ records the most recent time slot where a switch operation occurs. In Line 7, we solve $\\mathcal{P}^t_3$ to obtain the new hosting decisions. In Line 8, we invoke Algorithms 1 and 2 to get the other control decisions. Lines 9~10 decide whether a model switch operation occurs. In case of no model switch, then we are in Lines 11~13 and keep hosting the existing set of models that are being hosted. We still need to update the other control decisions as the inputs could be time-varying. The time complexity of Algorithm 4 is $O(T\\cdot N^2\\log(1/\\nu))$, based on our previous analysis of the time complexities of Algorithms 1 and 2.",
"translation": "$\\mathcal{P}^t_3$ 约束的系数矩阵是全幺模的 [72]。因此，我们可以用任意标准线性规划求解器在决策变量取值于 $[0,1]$ 的情况下求解 $\\mathcal{P}^t_3$，而得到的最优解会自动落在 $\\{0,1\\}$ 中。算法 4 在第 6 行采用了上述思路，其中 $k$ 是预设参数。我们另定义 $C^t_{SC}(y^t,y^{t-1})=\\sum_n\\Delta^t_n u^t_n[y^t_n-y^{t-1}_n]^+$ 与 $C^t_{-SC}(x^t,y^t,z^t)=\\sum_n x^t_n c^t_n+\\sum_n y^t_n(v^t_n+u^t_n(1-\\Delta^t_n))+e^t z^t$。$\\hat{t}$ 记录最近一次发生切换操作的时隙。在第 7 行，我们求解 $\\mathcal{P}^t_3$ 以获得新的托管决策。在第 8 行，我们调用算法 1 与算法 2 得到其他控制决策。第 9∼10 行判断是否发生模型切换操作。若没有发生模型切换，则进入第 11∼13 行，继续保持托管当前正在托管的那批模型。由于输入可能时变，我们仍需更新其他控制决策。基于前面对算法 1 与算法 2 时间复杂度的分析，算法 4 的时间复杂度为 $O(T\\cdot N^2\\log(1/\\nu))$。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec4-01",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"note-sec4-01"
],
"translation_ids": [
"zh-note-sec4-01"
],
"source": "",
"translation": "**“懒惰切换”到底在比较什么（关键）。** 第 6 行的判据是
$k\\cdot C^t_{SC}(\\bar{y}^t,\\bar{y}^{t-1})\\;\\le\\;\\sum_{\\tau=\\hat{t}}^{t-1}C^\\tau_{-SC}(\\bar{x}^\\tau,\\bar{y}^\\tau,\\bar{z}^\\tau)$。
右边是自上次切换以来累计的“非切换”成本（购买＋托管＋自有模型托管），左边是本次切换成本乘以常数 $k$。
含义：只有当“继续托管下去累计花掉的钱”已经超过“切一次要花的钱的 $k$ 倍”时，才值得切换。$k$ 越大越保守（越少切换）。
这正是原文后文那句 $\\sum_t C^t_{SC}\\le\\frac1k\\sum_t C^t_{-SC}$ 的来源：把每次切换的决策条件沿时间累加，就得到“切换成本总量不超过非切换成本总量的 $1/k$”，从而把难管的切换成本折算成非切换成本的一个小倍数。",
"notes": {
"kind": "blue",
"origin": "source"
}
},
{
"id": "alg-4",
"type": "pseudocode",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"alg-4"
],
"translation_ids": [
"zh-alg-4"
],
"source": "Algorithm 4 Model Hosting Algorithm\n\nOutput: y_bar^t, z_bar^t\n\n 1 if t = 1 then\n 2 Initialize t_hat = 1, y_bar^0;\n 3 Obtain the optimal solution y_hat^1, z_bar^1 to P_3^1;\n 4 Given y_bar^1 = y_hat^1, obtain x_bar^1 by Algorithms 1 and 2;\n 5 else\n 6 if k * C_SC^t(y_bar^t, y_bar^(t-1)) <= sum_{tau=t_hat}^{t-1} C_-SC^tau(x_bar^tau, y_bar^tau, z_bar^tau) then\n 7 Obtain the optimal solution y_hat^t, z_bar^t to P_3^t;\n 8 Given y_bar^t = y_hat^t, get x_bar^t by Algorithms 1 and 2;\n 9 if y_bar^t != y_bar^(t-1) then\n10 t_hat = t;\n11 if t_hat < t then\n12 y_bar^t = y_bar^(t-1);\n13 Given y_bar^t, obtain x_bar^t by Algorithms 1 and 2 and obtain z_bar^t by solving P_3^t;",
"translation": "算法 4 模型托管算法\n\n输出：y_bar^t、z_bar^t\n\n 1 if t = 1 then\n 2 初始化 t_hat = 1、y_bar^0；\n 3 求 P_3^1 的最优解 y_hat^1、z_bar^1；\n 4 令 y_bar^1 = y_hat^1，用算法 1 与算法 2 得到 x_bar^1；\n 5 else\n 6 if k * C_SC^t(y_bar^t, y_bar^(t-1)) <= sum_{tau=t_hat}^{t-1} C_-SC^tau(x_bar^tau, y_bar^tau, z_bar^tau) then\n 7 求 P_3^t 的最优解 y_hat^t、z_bar^t；\n 8 令 y_bar^t = y_hat^t，用算法 1 与算法 2 得到 x_bar^t；\n 9 if y_bar^t != y_bar^(t-1) then\n10 t_hat = t；\n11 if t_hat < t then\n12 y_bar^t = y_bar^(t-1)；\n13 给定 y_bar^t，用算法 1 与算法 2 得到 x_bar^t，并通过求解 P_3^t 得到 z_bar^t；",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec4-02",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"note-sec4-02"
],
"translation_ids": [
"zh-note-sec4-02"
],
"source": "",
"translation": "**关于算法 4 伪代码的两点如实说明。** 第一，原文该框在本 PDF 中只印出了 Output，没有 Input 行（抽取文本与页面渲染一致）。我按原样保留，未替作者补一行 Input。
第二，第 11∼13 行的缩进在原文中与第 6 行的 `if` 并列（而非嵌套在其内）。我按抽取到的缩进层级保留；若要精确复现，请以原文第 7 页算法框为准。",
"notes": {
"kind": "blue",
"origin": "source"
}
},
{
"id": "sec4-003",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"sec4-003"
],
"translation_ids": [
"zh-sec4-003"
],
"source": "Our motivation for Algorithm 4 is to balance the cumulative switching cost $\\sum_t C^t_{SC}$ and the cumulative non-switching cost $\\sum_t C^t_{-SC}$, and control this balance by $k$. We want to intentionally establish the relationship of $\\sum_t C^t_{SC}\\le\\frac{1}{k}\\sum_t C^t_{-SC}$; that is, $\\sum_t C^t_{SC}+\\sum_t C^t_{-SC}\\le(1+\\frac{1}{k})\\sum_t C^t_{-SC}$. We consider the total cost to the non-switching cost only, and thus remove the concern on the switching cost which used to be hard to manage. Hereafter, we will further connect the non-switching cost to the offline optimum and prove the competitive ratio, as elaborated in our competitive analysis later.",
"translation": "算法 4 的动机是平衡累计切换成本 $\\sum_t C^t_{SC}$ 与累计非切换成本 $\\sum_t C^t_{-SC}$，并用 $k$ 控制这一平衡。我们希望有意建立关系 $\\sum_t C^t_{SC}\\le\\frac{1}{k}\\sum_t C^t_{-SC}$，即 $\\sum_t C^t_{SC}+\\sum_t C^t_{-SC}\\le(1+\\frac{1}{k})\\sum_t C^t_{-SC}$。这样我们就把总成本归结为非切换成本，从而消除了对历来难以处理的切换成本的顾虑。此后，我们将进一步把非切换成本与离线最优联系起来，并证明竞争比，详见后文的竞争性分析。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec4-sub-b",
"type": "heading",
"section": "第四节 模型托管与集成学习",
"source_page": 8,
"source_ids": [
"sec4-sub-b"
],
"translation_ids": [
"zh-sec4-sub-b"
],
"source": "B. Algorithm 5: Hedge-Based Ensemble Learning",
"translation": "B. 算法 5：基于 Hedge 的集成学习",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec4-004",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 8,
"source_ids": [
"sec4-004"
],
"translation_ids": [
"zh-sec4-004"
],
"source": "As the models are selected and specified by Algorithm 4, the key idea of Algorithm 5 is, for each given data sample, using each model to conduct inference and then combining these inference results as a weighted sum to produce the joint, final inference result that will be returned to the end user. Specifically, we adopt the Hedge algorithm [39] to update the weights in an exponential manner based on the loss between the inferred label of each model and the ground-truth label. Lines 4~6 conduct weight normalization. Line 8 produces the joint inference result. Lines 11~13 are the Hedge steps, preparing for the next data sample in the stream. The time complexity of Algorithm 5 is $O(NM^t)$, where the loops in Lines 4 and 11 have $N$ iterations, and Line 2 has $M^t$ iterations.",
"translation": "由于模型已由算法 4 选定，算法 5 的核心思路是：对每个给定的数据样本，用各模型分别执行推理，再把这些推理结果以加权和的形式合并，产生最终返回给终端用户的联合推理结果。具体而言，我们采用 Hedge 算法 [39]，依据各模型的推理标签与真实标签之间的损失，以指数方式更新权重。第 4∼6 行做权重归一化；第 8 行产生联合推理结果；第 11∼13 行是 Hedge 步骤，为数据流中的下一个样本做准备。算法 5 的时间复杂度为 $O(NM^t)$，其中第 4 行与第 11 行的循环各迭代 $N$ 次，第 2 行迭代 $M^t$ 次。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "alg-5",
"type": "pseudocode",
"section": "第四节 模型托管与集成学习",
"source_page": 7,
"source_ids": [
"alg-5"
],
"translation_ids": [
"zh-alg-5"
],
"source": "Algorithm 5 Ensemble Learning Algorithm\n\nInput : y_bar^t, z_bar^t, data samples M^t, step size mu^t_m, for all m\nOutput: Inferred labels b_hat^t_m, for all m\n\n 1 Initialize weight parameters: xi^t_{n,1} = y_bar^t_n, psi^t_1 = z_bar^t\n 2 for m = 1 to M^t do\n 3 > Weights update\n 4 for n = 1 to N do\n 5 alpha^t_{n,m} = xi^t_{n,m} / (sum_n xi^t_{n,m} + psi^t_m), y_bar^t_n = 1\n 0, y_bar^t_n = 0\n 6 beta^t_m = psi^t_m / (sum_n xi^t_{n,m} + psi^t_m), z_bar^t = 1\n 0, z_bar^t = 0\n 7 > Label inference\n 8 b_hat^t_m = sum_n alpha^t_{n,m} h^t_n(a^t_m) + beta^t_m h^t(a^t_m);\n 9 > Weight parameters update\n10 receive the ground-truth label b^t_m;\n11 for n = 1 to N do\n12 xi^t_{n,m+1} = xi^t_{n,m} exp{-mu^t_m l(h^t_n(a^t_m), b^t_m)};\n13 psi^t_{m+1} = psi^t_m exp{-mu^t_m l(h^t(a^t_m), b^t_m)};",
"translation": "算法 5 集成学习算法\n\n输入：y_bar^t、z_bar^t、数据样本 M^t、步长 mu^t_m（对所有 m）\n输出：推理标签 b_hat^t_m（对所有 m）\n\n 1 初始化权重参数：xi^t_{n,1} = y_bar^t_n，psi^t_1 = z_bar^t\n 2 for m = 1 to M^t do\n 3 ▷ 权重更新\n 4 for n = 1 to N do\n 5 alpha^t_{n,m} = xi^t_{n,m} / (sum_n xi^t_{n,m} + psi^t_m)， 当 y_bar^t_n = 1\n 0， 当 y_bar^t_n = 0\n 6 beta^t_m = psi^t_m / (sum_n xi^t_{n,m} + psi^t_m)， 当 z_bar^t = 1\n 0， 当 z_bar^t = 0\n 7 ▷ 标签推理\n 8 b_hat^t_m = sum_n alpha^t_{n,m} h^t_n(a^t_m) + beta^t_m h^t(a^t_m)；\n 9 ▷ 权重参数更新\n10 接收真实标签 b^t_m；\n11 for n = 1 to N do\n12 xi^t_{n,m+1} = xi^t_{n,m} exp{-mu^t_m l(h^t_n(a^t_m), b^t_m)}；\n13 psi^t_{m+1} = psi^t_m exp{-mu^t_m l(h^t(a^t_m), b^t_m)}；",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec4-03",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 8,
"source_ids": [
"note-sec4-03"
],
"translation_ids": [
"zh-note-sec4-03"
],
"source": "",
"translation": "**算法 5 的三处设计要点。** ① 权重用“未归一化的正数” $\\xi$、$\\psi$ 累积，每步再除以总和得到 $\\alpha$、$\\beta$（第 5、6 行）——这是 Hedge 的标准做法：乘性更新会迅速把小权重压到近乎 0，从而自动“淘汰”差模型。
② 初始化 $\\xi^t_{n,1}=\\bar{y}^t_n$、$\\psi^t_1=\\bar{z}^t$：只有被托管（$y=1$）的模型才有非零初始权重，这保证“没托管的模型权重恒为 0”，与约束 (1d)(1e) 一致。
③ 第 10 行“接收真实标签”夹在第 8 行（推理）与第 12、13 行（更新）之间：这明确体现了“先推理、后拿标签”的在线设定——更新只能用已完成推理的样本。",
"notes": {
"kind": "green",
"origin": "source"
}
},
{
"id": "sec4-sub-c",
"type": "heading",
"section": "第四节 模型托管与集成学习",
"source_page": 8,
"source_ids": [
"sec4-sub-c"
],
"translation_ids": [
"zh-sec4-sub-c"
],
"source": "C. Loss and Competitiveness Analysis",
"translation": "C. 损失与竞争性分析",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec4-005",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 8,
"source_ids": [
"sec4-005"
],
"translation_ids": [
"zh-sec4-005"
],
"source": "We show that the inference loss cumulatively incurred by our ensemble learning algorithm upon the entire data stream could be no worse than a parameterized constant times the sum of the optimal loss in each time slot incurred by the single best model out of the selected models for that time slot. We also define the competitive ratio and exhibit that our proposed approach leads to a parameterized-constant competitive ratio. We introduce some additional notations. We write the social cost as $C=\\sum_t(C^t_L+C^t_{-L})=\\sum_t(C^t_L+C^t_{SC}+C^t_{-SC})$, where $C^t_L=\\sum_m((\\sum_n\\alpha^t_{n,m}h^t_n(a^t_m)+\\beta^t_mh^t(a^t_m))-b^t_m)^2$ is the loss at $t$, and $C^t_{-L}=C^t_{SC}+C^t_{-SC}$ is the non-loss social cost at $t$; and $C^t_{SC}$ and $C^t_{-SC}$ are as in Section IV-A.",
"translation": "我们证明：集成学习算法在整个数据流上累计产生的推理损失，不会比“每个时隙中，所选模型里单个最佳模型在该时隙产生的最优损失之和”的某个参数化常数倍更差。我们还定义竞争比，并表明所提方法可达到参数化常数的竞争比。我们引入一些额外记号。把社会成本写成 $C=\\sum_t(C^t_L+C^t_{-L})=\\sum_t(C^t_L+C^t_{SC}+C^t_{-SC})$，其中 $C^t_L=\\sum_m((\\sum_n\\alpha^t_{n,m}h^t_n(a^t_m)+\\beta^t_mh^t(a^t_m))-b^t_m)^2$ 是 $t$ 时刻的损失，$C^t_{-L}=C^t_{SC}+C^t_{-SC}$ 是 $t$ 时刻的非损失社会成本；$C^t_{SC}$ 与 $C^t_{-SC}$ 的定义同第四节 A。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec4-thm-3",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 8,
"source_ids": [
"sec4-thm-3"
],
"translation_ids": [
"zh-sec4-thm-3"
],
"source": "**Theorem 3:** With $\\mu^t_m=\\sqrt{8\\ln I_t/m}$, we have $\\sum_t C^t_L\\le\\sum_t C^{t*}_L[1+\\theta_1(2\\sum_t\\ln I_t+\\sqrt{\\frac{M^t}{8}\\sum_t\\ln I_t})]$. $I_t$ is the number of the models hosted at $t$. $C^t_L$ is the loss incurred jointly by the $I_t$ models as in Algorithm 5 upon the data samples $\\mathcal{M}^t$. $C^{t*}_L$ is the optimal loss incurred by the single best model out of the $I_t$ models upon the data samples $\\mathcal{M}^t$, assuming $\\sum_t C^{t*}_L\\ge1>0$ where $\\theta_1\\ne0$ is a constant. Proof: See Appendix C in our supplementary material. $\\square$",
"translation": "**定理 3：** 取 $\\mu^t_m=\\sqrt{8\\ln I_t/m}$，则有 $\\sum_t C^t_L\\le\\sum_t C^{t*}_L[1+\\theta_1(2\\sum_t\\ln I_t+\\sqrt{\\frac{M^t}{8}\\sum_t\\ln I_t})]$。其中 $I_t$ 是 $t$ 时刻托管的模型数；$C^t_L$ 是算法 5 中这 $I_t$ 个模型在数据样本 $\\mathcal{M}^t$ 上联合产生的损失；$C^{t*}_L$ 是这 $I_t$ 个模型中单个最佳模型在数据样本 $\\mathcal{M}^t$ 上产生的最优损失；并假设 $\\sum_t C^{t*}_L\\ge1>0$，其中 $\\theta_1\\ne0$ 为常数。证明：见补充材料附录 C。$\\square$",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "note-sec4-04",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 8,
"source_ids": [
"note-sec4-04"
],
"translation_ids": [
"zh-note-sec4-04"
],
"source": "",
"translation": "**关于定理 3 公式的重建说明（须留意）。** 原文该式在双栏排版中与右栏正文逐字符交错（例如同一行里既含 $\\ln I_t$ 又含 “The Spam dataset contains…”）。上式中 $\\theta_1$ 括号内 $2\\sum_t\\ln I_t+\\sqrt{\\frac{M^t}{8}\\sum_t\\ln I_t}$ 的求和范围与 $M^t$、$8$ 的确切位置是我依据 Hedge 算法的标准遗憾界结构反推的，不能保证与原文逐字符一致。阅读该式时请以原 PDF 第 8 页为准；这一点已记入 `math-audit.md`。",
"notes": {
"kind": "blue",
"origin": "source"
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},
{
"id": "sec4-thm-4",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 8,
"source_ids": [
"sec4-thm-4"
],
"translation_ids": [
"zh-sec4-thm-4"
],
"source": "**Theorem 4:** Our entire proposed approach is \"$r$-competitive\" for the problem $\\mathcal{P}_0$. If we use $C$ to denote the objective value of $\\mathcal{P}_0$ incurred by our approach, and $C^*$ to denote the sum of the social cost (except the loss) in the offline optimum of $\\mathcal{P}_0$ plus the cumulative per-time-slot optimal loss incurred by the single best model out of the selected models in each corresponding time slot, then we have $C\\le rC^*$, where $r=\\max\\{r_1,r_2\\}$, $r_1=1+\\theta_1\\rho(2+\\frac{1}{2}\\sqrt{\\sum_t M^t\\ln I_t})$, and $r_2$ is defined by $R_T$, $k_2$ and $\\min_t I_t$ as implied by Algorithm 4, assuming $\\sum_t C^{t*}_L\\ge1>0$ where $\\theta_2\\ne0$ is a constant; $k_2$ is the constant in Algorithm 4; and $\\rho$ and $R_T$ are also constants. Proof: See Appendix D in our supplementary material. $\\square$",
"translation": "**定理 4：** 我们所提出的整套方法对问题 $\\mathcal{P}_0$ 是“$r$-竞争的”。若用 $C$ 表示本方法在 $\\mathcal{P}_0$ 上产生的目标值，用 $C^*$ 表示“$\\mathcal{P}_0$ 离线最优中的社会成本（不含损失）”加上“各对应时隙中所选模型里单个最佳模型逐时隙产生的最优损失的累加”，则有 $C\\le rC^*$，其中 $r=\\max\\{r_1,r_2\\}$，$r_1=1+\\theta_1\\rho(2+\\frac{1}{2}\\sqrt{\\sum_t M^t\\ln I_t})$，而 $r_2$ 由 $R_T$、$k_2$ 与 $\\min_t I_t$ 依照算法 4 的含义确定；并假设 $\\sum_t C^{t*}_L\\ge1>0$，其中 $\\theta_2\\ne0$ 为常数；$k_2$ 是算法 4 中的常数；$\\rho$ 与 $R_T$ 也是常数。证明：见补充材料附录 D。$\\square$",
"notes": {
"kind": null,
"origin": "source"
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},
{
"id": "note-sec4-05",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 8,
"source_ids": [
"note-sec4-05"
],
"translation_ids": [
"zh-note-sec4-05"
],
"source": "",
"translation": "**关于定理 4 的 $r_1$、$r_2$ 的重建说明（须留意）。** 原文中 $r_1$ 与 $r_2$ 的表达式同样因双栏交错而无法可靠逐字符恢复：抽取到的片段为 “$r_1=1+\\theta_1\\rho(2+\\frac12\\sqrt{\\cdots})$” 与 “$r_2=\\theta_2(\\cdots)$，含有 $R_T$、$k_2$、$\\min_t I_t$”。上文给出的是结构级重建（常数 $\\theta_1,\\theta_2,\\rho,R_T$、切换常数 $k_2$、$\\min_t I_t$ 的相对位置），其中 $r_1$ 的被开方项我按 $\\sum_t M^t\\ln I_t$ 填写。**凡引用该定理的常数形式，请核对原 PDF 第 8 页。** 已记入 `math-audit.md`。",
"notes": {
"kind": "blue",
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},
{
"id": "sec4-006",
"type": "paragraph",
"section": "第四节 模型托管与集成学习",
"source_page": 8,
"source_ids": [
"sec4-006"
],
"translation_ids": [
"zh-sec4-006"
],
"source": "Theorem 4 captures the competitive ratio and thus the multiplicative gap between the objective value of $\\mathcal{P}_0$ incurred by our proposed online approach and that of $\\mathcal{P}_0$ in a particularly specified case. This particular case is that we use the social cost (except the inference loss) from the offline optimum of $\\mathcal{P}_0$, and use the inference loss incurred cumulatively by the per-time-slot single best model out of the ensemble in each time slot, where the ensemble is chosen as in the offline optimum of $\\mathcal{P}_0$. Alternatively, one may want to quantify the multiplicative gap between our approach and the offline optimum of $\\mathcal{P}_0$ directly; if so, in the offline optimum of $\\mathcal{P}_0$, the inference loss is incurred by the best ensemble which may vary dynamically as time goes. Here, we choose not to directly compare to the offline optimum of $\\mathcal{P}_0$ in order to get aligned with the convention of the \"learning from experts\" setting [39]. The comparison to the offline optimum of $\\mathcal{P}_0$ can be of independent interest, which we would like to postpone to future work.",
"translation": "定理 4 刻画了竞争比，也就是“本文在线方法在 $\\mathcal{P}_0$ 上产生的目标值”与“某一特定指定情形下 $\\mathcal{P}_0$ 的目标值”之间的乘性差距。这一特定情形是：社会成本（不含推理损失）取自 $\\mathcal{P}_0$ 的离线最优，而推理损失取自“每个时隙中、按照 $\\mathcal{P}_0$ 离线最优所选集成里单个最佳模型”在该时隙累计产生的损失。换一种做法，人们也许想直接量化本方法与 $\\mathcal{P}_0$ 离线最优之间的乘性差距；若如此，在 $\\mathcal{P}_0$ 的离线最优中，推理损失由随时间动态变化的最佳集成产生。此处我们选择不直接与 $\\mathcal{P}_0$ 的离线最优比较，以与“从专家中学习”这一设定的惯例保持一致 [39]。与 $\\mathcal{P}_0$ 离线最优的比较本身具有独立的研究价值，我们希望留待未来工作。",
"notes": {
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},
{
"id": "sec5-heading",
"type": "heading",
"section": "第五节 实验研究",
"source_page": 8,
"source_ids": [
"sec5-heading"
],
"translation_ids": [
"zh-sec5-heading"
],
"source": "V. EXPERIMENTAL STUDY",
"translation": "第五节 实验研究",
"notes": {
"kind": null,
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},
{
"id": "sec5-sub-a",
"type": "heading",
"section": "第五节 实验研究",
"source_page": 8,
"source_ids": [
"sec5-sub-a"
],
"translation_ids": [
"zh-sec5-sub-a"
],
"source": "A. Experimental Settings",
"translation": "A. 实验设置",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec5-001",
"type": "paragraph",
"section": "第五节 实验研究",
"source_page": 8,
"source_ids": [
"sec5-001"
],
"translation_ids": [
"zh-sec5-001"
],
"source": "Datasets: We use two real-world datasets and two widely-used benchmark datasets, all with concept drifts [22], [23], [24], [25], [26].",
"translation": "数据集：我们使用两个真实世界数据集和两个被广泛使用的基准数据集，它们全都存在概念漂移 [22], [23], [24], [25], [26]。",
"notes": {
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{
"id": "sec5-002",
"type": "list-item",
"section": "第五节 实验研究",
"source_page": 8,
"source_ids": [
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"translation_ids": [
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],
"source": "The Posture dataset contains 164,860 data samples from a sensor carried by 5 different people one after another. The task is to predict which movement is performed, among the 11 classes. This dataset was artificially injected with concept drifts according to Reis et al. [42] in 2016.",
"translation": "Posture 数据集包含 164,860 个数据样本，来自由 5 个不同的人依次佩戴的传感器。任务是在 11 个类别中预测执行的是哪一个动作。该数据集按照 Reis 等人 [42] 的方法于 2016 年被人为注入了概念漂移。",
"notes": {
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},
{
"id": "sec5-003",
"type": "list-item",
"section": "第五节 实验研究",
"source_page": 8,
"source_ids": [
"sec5-003"
],
"translation_ids": [
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],
"source": "The Rialto dataset consists of 82,250 data samples from time-lapse videos of a webcam and 10 classes [41]. Each data sample is a normalized 27-dimensional RGB histogram (i.e., 27 features), and the 10 classes correspond to 10 colorful buildings next to the Rialto bridge in Venice, Italy in 2016. The task is classification. Concept drifts exist as the changing weather and lighting conditions affect the color-based representation.",
"translation": "Rialto 数据集由来自网络摄像头延时视频的 82,250 个数据样本和 10 个类别组成 [41]。每个数据样本是一个归一化的 27 维 RGB 直方图（即 27 个特征），这 10 个类别对应于 2016 年意大利威尼斯里亚托桥旁 10 座色彩鲜艳的建筑。任务是分类。由于天气与光照条件的变化会影响基于颜色的表示，因此存在概念漂移。",
"notes": {
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{
"id": "sec5-004",
"type": "list-item",
"section": "第五节 实验研究",
"source_page": 8,
"source_ids": [
"sec5-004"
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"translation_ids": [
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],
"source": "The Spam dataset contains 9,324 email messages (20% spam emails and 80% legitimate emails) derived from the Spam Assassin collection. This data set contains 500 features, which were retrieved using the chi-square feature-selection approach. It has been considered a typical gradual drift dataset since Katakis et al. [43]. The task is to predict an email is spam or legitimate.",
"translation": "Spam 数据集包含 9,324 封电子邮件（20% 为垃圾邮件、80% 为正常邮件），取自 Spam Assassin 语料库。该数据集包含 500 个特征，这些特征是用卡方特征选择方法提取的。自 Katakis 等人 [43] 以来，它一直被视为典型的渐变漂移数据集。任务是预测一封邮件是垃圾邮件还是正常邮件。",
"notes": {
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{
"id": "sec5-005",
"type": "list-item",
"section": "第五节 实验研究",
"source_page": 8,
"source_ids": [
"sec5-005"
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"translation_ids": [
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"source": "The Electricity dataset contains 45,312 instances, collected every 30 minutes from the Australian New South Wales Electricity Market between May 1996 and December 1998 [44]. This data set contains 8 features and 2 classes and has been widely used for concept drift adaptation evaluations. The task is to predict the change of the price (i.e., up and down).",
"translation": "Electricity 数据集包含 45,312 个实例，采集自 1996 年 5 月至 1998 年 12 月期间的澳大利亚新南威尔士州电力市场，采样间隔为 30 分钟 [44]。该数据集包含 8 个特征和 2 个类别，被广泛用于概念漂移自适应的评估。任务是预测价格的变化（即上涨与下跌）。",
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"id": "note-sec5-01",
"type": "paragraph",
"section": "第五节 实验研究",
"source_page": 8,
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"translation": "**四个数据集与漂移来源。** 按原文说法，其中 Posture 与 Rialto 属“真实世界数据集”，Spam 与 Electricity 属“基准数据集”。
1）**Posture**：可穿戴传感器的人体动作数据，漂移是**人为注入**的（按 Reis 等人 [42] 的方法，2016 年）。
2）**Rialto**：网络摄像头延时视频的颜色直方图，漂移来自**天气与光照变化**对颜色表示的影响，属自然漂移。
3）**Spam**：邮件文本特征，被视作典型的**渐变漂移**数据集。
4）**Electricity**：电力市场价格，按 30 分钟采样，漂移来自电力市场本身的时序变化。
这四个数据集共同的实验意义是：数据分布会随时间变化，因此需要一个能持续调整模型组合（集成权重、托管集合）的方法，而不是一次训练后固定不变的模型。",
"notes": {
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{
"id": "sec5-006",
"type": "paragraph",
"section": "第五节 实验研究",
"source_page": 8,
"source_ids": [
"sec5-006"
],
"translation_ids": [
"zh-sec5-006"
],
"source": "Models: We consider 8 ∼ 64 model providers, and divide the first 80% data evenly into 8 ∼ 64 pieces and train the models correspondingly. We use the rest 20% data as the data stream for the service provider, arriving in a uniform manner. Without loss of generality, we adopt the decision trees as the models in our evaluations (unless otherwise specified), aligned with lots of existing ensemble learning research [21], [25], [26]; specifically, we consider the Classification And Regression Tree (CART) [73]. We also consider the Support Vector Machine (SVM) [21], [74] and the Multilayer Perceptron (MLP) (as in deep learning) as other base models for comparison. We consider $|T|=100$ minutes, with 1 minute per time slot.",
"translation": "模型：我们考虑 8 ∼ 64 个模型提供方，把前 80% 的数据均匀划分为 8 ∼ 64 份，并相应地训练模型。我们把其余 20% 的数据作为服务提供方的数据流，这些数据以均匀方式到达。不失一般性，我们在评估中采用决策树作为模型（除非另有说明），这与大量已有的集成学习研究 [21], [25], [26] 一致；具体而言，我们考虑分类与回归树（CART）[73]。我们还考虑支持向量机（SVM）[21], [74] 以及多层感知机（MLP）（如深度学习中所用）作为其他基模型以作比较。我们考虑 $|T|=100$ 分钟，每个时隙为 1 分钟。",
"notes": {
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},
{
"id": "sec5-007",
"type": "paragraph",
"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
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],
"translation_ids": [
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],
"source": "Costs and Bids: We consider the Alibaba Cloud [45] of 29 regions and 88 availability zones worldwide [46], with each region often having multiple availability zones. We choose Beijing, China as the location of the service provider's cloud, and use all the other regions with their 76 availability zones as the model providers' clouds (and we consider up to 64 of them), where each availability zone corresponds to a model provider. We can thus use the geographical distance to estimate the network delay as the model downloading cost. We use the electricity cost as the model hosting cost, following the hourly real-time electricity prices of ComEd in January, 2024 [47]. The participation threshold of model providers is uniformly generated in [0, 1] [17], [20], and the service provider's maximum number of models that can be purchased from each auction is in [6, 10]. The bidding price is from [5, 18] $, following the electricity consumption for model training [48]. The model variation indicator is set to 1 (i.e., model unchanged) by default, unless otherwise noted.",
"translation": "成本与投标：我们考虑 Alibaba Cloud [45]，它在全球有 29 个地域（region）和 88 个可用区（availability zone）[46]，每个地域通常有多个可用区。我们选择中国北京作为服务提供方云的位置，并把其余所有地域及其 76 个可用区作为模型提供方的云（我们最多考虑其中 64 个），其中每个可用区对应一个模型提供方。这样，我们便可以用地理距离来估计网络时延，作为模型下载成本。我们按 ComEd 在 2024 年 1 月的逐时实时电价 [47]，采用电费作为模型托管成本。模型提供方的参与阈值在 $[0,1]$ 中均匀生成 [17], [20]，服务提供方在每场拍卖中最多可购买的模型数量在 $[6,10]$ 之间。投标价格取自 $[5,18]$ 美元，其依据是模型训练的电能消耗 [48]。除非另有说明，模型变化指示量默认设为 1（即模型不变）。",
"notes": {
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},
{
"id": "sec5-008",
"type": "paragraph",
"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
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],
"translation_ids": [
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],
"source": "Algorithms: We implement multiple algorithms.",
"translation": "算法：我们实现了多种算法。",
"notes": {
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},
{
"id": "sec5-009",
"type": "list-item",
"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
"sec5-009"
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"translation_ids": [
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],
"source": "Proposed: Our proposed approach, which uses the Hedge ensemble method to update the weights for the models.",
"translation": "Proposed：我们提出的方法，它使用 Hedge 集成方法更新各模型的权重。",
"notes": {
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},
{
"id": "sec5-010",
"type": "list-item",
"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
"sec5-010"
],
"translation_ids": [
"zh-sec5-010"
],
"source": "Random: The approach that selects bids randomly in each time slot, where the model hosting decisions directly follow the bid selection decisions with equal and constant weight for each deployed model.",
"translation": "Random：在每个时隙随机选择投标的方法；其中模型托管决策直接跟随投标选择决策，并且为每个已部署模型赋予相等且恒定的权重。",
"notes": {
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"id": "sec5-011",
"type": "list-item",
"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
"sec5-011"
],
"translation_ids": [
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"source": "Greedy: The approach that optimizes the one-shot slice of our original problem in each individual time slot, i.e., deciding the models to host by solving $\\mathcal{P}^t_3$ at each $t$, uses the same algorithms as our proposed approach for bid and payment determination, and employs equal and constant weight for each hosted model.",
"translation": "Greedy：在每个单独的时隙中优化原问题的单时隙切片的方法，即在每个 $t$ 通过求解 $\\mathcal{P}^t_3$ 决定要托管的模型；它在投标与支付确定上使用与我们所提方法相同的算法，并对每个被托管的模型采用相等且恒定的权重。",
"notes": {
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},
{
"id": "sec5-012",
"type": "list-item",
"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
"sec5-012"
],
"translation_ids": [
"zh-sec5-012"
],
"source": "DTEL+: The greedy approach above using the state-of-the-art ensemble learning algorithm DTEL [25] to update the weights for the models. This approach calculates the weight based on the mean squared error, updates the weight for each model only after processing all the data samples in a time slot, and produces the inference result of the ensemble by combining that of each model via a weighted voting scheme.",
"translation": "DTEL+：上述贪心方法，但使用前沿的集成学习算法 DTEL [25] 来更新各模型的权重。该方法基于均方误差计算权重，仅在处理完一个时隙内的全部数据样本之后才更新每个模型的权重，并通过加权投票方案把各模型的结果组合起来以产生集成的推理结果。",
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"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
"sec5-013"
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"translation_ids": [
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"source": "DES+: The greedy approach above using the state-of-the-art ensemble learning algorithm with dynamic ensemble selection [22]. For each data sample, this approach finds its nearest neighbors within the set of the data samples in the last time slot, uses the models that can correctly classify these nearest neighbors to construct the ensemble, and produces the inference result of the ensemble via a soft majority voting scheme.",
"translation": "DES+：上述贪心方法，但使用带动态集成选择的前沿集成学习算法 [22]。对每个数据样本，该方法在上一时隙的数据样本集合中寻找其最近邻，使用能够正确分类这些最近邻的模型来构造集成，并通过软多数投票方案产生集成的推理结果。",
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"id": "sec5-014",
"type": "list-item",
"section": "第五节 实验研究",
"source_page": 9,
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"source": "Offline: The offline optimum of our original problem solved via the Gurobi [75] solver, with all the inputs in the entire time horizon known in advance.",
"translation": "Offline：用 Gurobi [75] 求解器求得的原问题的离线最优解，其中整个时间范围内的全部输入都是事先已知的。",
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"id": "note-sec5-02",
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"section": "第五节 实验研究",
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"translation": "**五类基线方法分别“去掉”了我们方法的哪一部分。**
• **Random**：投标随机选，托管决策跟着投标走，权重恒定——相当于完全不做优化。
• **Greedy**：每个时隙都重新求解一次单时隙最优（$\\mathcal{P}^t_3$），因此**没有考虑切换成本跨时隙的耦合**，可能频繁改动托管集合。
• **DTEL+ / DES+**：托管部分沿用 Greedy，但把集成权重更新换成两种前沿的集成学习算法。DTEL+ 是**按整个时隙批量**用均方误差算权重；DES+ 是**逐样本**用最近邻挑模型再软投票。
• **Offline**：在事先知道全部输入的前提下用 Gurobi 求得的离线最优，是**只用于对照、在线算法无法达到**的下界参照（图中“离离线最优最近”即指此）。
这样安排的用意是：把“在线决策（投标与托管）”和“集成学习（权重更新）”两部分的效果分开观察。",
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"section": "第五节 实验研究",
"source_page": 9,
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"source": "B. Experimental Results",
"translation": "B. 实验结果",
"notes": {
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{
"id": "sec5-015",
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"section": "第五节 实验研究",
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"source": "Fig. 5 shows the normalized social cost of different algorithms in the cumulative manner as time goes, when there are 8 bids in every auction. Our approach shows a slower growth trend of the cumulative social cost than all others, and is the closest to the offline optimum. We have also conducted the evaluations on the real-time cumulative social cost for 16, 32, 48, and 64 bids, respectively, and they show similar trends.",
"translation": "图 5 展示了每场拍卖有 8 个投标时，不同算法随时间的归一化社会成本的累积变化。与所有其他方法相比，我们的方法呈现出更慢的累积社会成本增长趋势，并且最接近离线最优。我们还分别对 16、32、48、64 个投标的情形评估了实时累积社会成本，它们呈现出相似的趋势。",
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"id": "fig-5-caption",
"type": "caption",
"section": "第五节 实验研究",
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"source": "Fig. 5. Social cost.",
"translation": "图 5 社会成本。",
"notes": {
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{
"id": "fig-6-caption",
"type": "caption",
"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
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"source": "Fig. 6. Scalability.",
"translation": "图 6 可扩展性。",
"notes": {
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{
"id": "fig-7-caption",
"type": "caption",
"section": "第五节 实验研究",
"source_page": 9,
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"source": "Fig. 7. Impact of hosting budget.",
"translation": "图 7 托管预算的影响。",
"notes": {
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{
"id": "sec5-016",
"type": "paragraph",
"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
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"source": "Fig. 6 presents the normalized average social cost of different algorithms. As the number of bidders increases, compared to Random, Greedy, DTEL+, and DES+, our approach reduces the social cost on average by 70%, 37%, 35%, and 46%, respectively. Note that even though DES+ has better inference accuracy than DTEL+, the former incurs larger loss when its inference is incorrect, thus greater social cost. The empirical competitive ratio of our approach is 2.1∼2.7. The social cost of our approach decreases as the number of bidders grows because there are more bids to choose from for further cost reduction, which shows the scalability of our approach.",
"translation": "图 6 给出了不同算法的归一化平均社会成本。随着投标者数量增加，与 Random、Greedy、DTEL+ 和 DES+ 相比，我们的方法平均分别把社会成本降低了 70%、37%、35% 和 46%。注意，尽管 DES+ 的推理精度优于 DTEL+，但前者在推理出错时会产生更大的损失，因而社会成本更高。我们方法的经验竞争比为 2.1∼2.7。随着投标者数量增长，我们方法的社会成本下降，因为可供选择的投标更多、从而能进一步降低成本，这体现了我们方法的可扩展性。",
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"id": "note-sec5-03",
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"section": "第五节 实验研究",
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"translation": "**“降低 70%、37%、35%、46%”应如何理解。** 这些数字是**同一个量（归一化平均社会成本）在本方法与其各自基线之间取平均后算出的相对降幅**，四个数字分别对应 Random、Greedy、DTEL+、DES+，彼此不是同一分档的连续比较，不能相加或相乘。
另外注意原文对 DES+ 的说明：精度更高并不必然带来更低的社会成本，因为社会成本还包含**推理出错时的损失幅度**；DES+ 出错时损失更大，所以社会成本反而高于 DTEL+。这正说明本文的目标函数是“成本 + 推理损失”的联合优化，而不是单纯追求精度。
“经验竞争比 2.1∼2.7”是实测得到的、覆盖不同投标者数量的区间，用来与理论上的参数化常数竞争比相互印证。",
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"id": "sec5-017",
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"section": "第五节 实验研究",
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"source": "Fig. 7 shows the impact of the model hosting budget on the normalized average social cost. As more models are allowed to be hosted, the social cost increases for all algorithms; and ours still incurs the lowest social cost, except the offline optimum.",
"translation": "图 7 展示了模型托管预算对归一化平均社会成本的影响。随着允许托管的模型数量增加，所有算法的社会成本都上升；而除离线最优之外，我们的方法仍然产生最低的社会成本。",
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{
"id": "sec5-018",
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"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
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"source": "Fig. 8 verifies the truthfulness of our auction mechanism. We select two bids randomly as the example. As shown, if the bid bids its true cost, i.e., 7$ and 10$, respectively, then it achieves the highest utility. The utility could drop vastly if the bidding price is not the same as the true cost.",
"translation": "图 8 验证了我们拍卖机制的真实性。我们随机选取两个投标作为示例。如图所示，如果投标按真实成本报价，即分别为 7 美元和 10 美元，那么它能获得最高效用。若投标价格与真实成本不一致，效用可能会大幅下降。",
"notes": {
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{
"id": "sec5-019",
"type": "paragraph",
"section": "第五节 实验研究",
"source_page": 9,
"source_ids": [
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"translation_ids": [
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"source": "Fig. 9 checks the individual rationality of our auction mechanism. We randomly select two bids and record the changes of their bidding price and corresponding payments over 10 consecutive slots. We see that the payment received is always no less than the bidding price. Note that when a bid does not win in an auction, the payment defaults to zero.",
"translation": "图 9 检验了我们拍卖机制的个体理性。我们随机选取两个投标，并记录它们在连续 10 个时隙上的投标价格及相应支付的变化。我们看到，所收到的支付始终不低于投标价格。注意，当一个投标在某场拍卖中未获胜时，其支付默认为零。",
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{
"id": "sec5-020",
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"section": "第五节 实验研究",
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"source": "Fig. 10 and Fig. 11 exhibit the dynamic regret and the dynamic fit of different algorithms for P1, as the total length of the time horizon varies. Our approach has the lowest dynamic regret and fit, also confirming that our regret and fit grow only sub-linearly with time, aligning with our theoretical analysis.",
"translation": "图 10 与图 11 展示了随着时间范围总长度变化，不同算法在 P1 上的动态遗憾与动态拟合。我们的方法具有最低的动态遗憾与动态拟合，这也证实了我们的遗憾与拟合仅随时间次线性增长，与我们的理论分析一致。",
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"id": "fig-8-caption",
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"source_page": 10,
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"source": "Fig. 8. Utility.",
"translation": "图 8 效用。",
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{
"id": "fig-9-caption",
"type": "caption",
"section": "第五节 实验研究",
"source_page": 10,
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"source": "Fig. 9. Payment vs. cost.",
"translation": "图 9 支付与成本的对比。",
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{
"id": "fig-10-caption",
"type": "caption",
"section": "第五节 实验研究",
"source_page": 10,
"source_ids": [
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"source": "Fig. 10. Dynamic regret.",
"translation": "图 10 动态遗憾。",
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{
"id": "fig-11-caption",
"type": "caption",
"section": "第五节 实验研究",
"source_page": 10,
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"source": "Fig. 11. Dynamic fit.",
"translation": "图 11 动态拟合。",
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{
"id": "fig-12-caption",
"type": "caption",
"section": "第五节 实验研究",
"source_page": 10,
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"source": "Fig. 12. Impact of model change.",
"translation": "图 12 模型变化的影响。",
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{
"id": "sec5-021",
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"section": "第五节 实验研究",
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"source": "Fig. 12 illustrates how model variations can impact the social cost. In our experiments, we simulate model variations as the model provider using the additional training data from another model provider to update its own model. When models in the market undergo such updates, the social cost exhibits less fluctuation compared to the social cost of models that are static. This is because updated models could more easily adapt to data streams, thereby minimizing the inference loss.",
"translation": "图 12 说明了模型变化如何影响社会成本。在我们的实验中，我们把模型变化模拟为：模型提供方使用来自另一个模型提供方的额外训练数据来更新自己的模型。当市场中的模型经历此类更新时，与静态模型的社会成本相比，社会成本的波动更小。这是因为更新后的模型能更容易地适应数据流，从而使推理损失最小化。",
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"id": "sec5-022",
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"source": "Fig. 13 evaluates the inference accuracy in each time slot over the entire data stream of the Posture data. The results for other datasets are similar. Our approach not only achieves the highest accuracy in all the time slots, but is also relatively more stable; the accuracy results of other algorithms fluctuate dramatically and are more sensitive to the concept drift.",
"translation": "图 13 评估了在 Posture 数据的整个数据流上每个时隙的推理精度。其他数据集的结果类似。我们的方法不仅在所有时隙都达到最高精度，而且相对更稳定；其他算法的精度结果波动剧烈，并且对概念漂移更为敏感。",
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"id": "fig-13-caption",
"type": "caption",
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"source": "Fig. 13. Real-time accuracy.",
"translation": "图 13 实时精度。",
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{
"id": "fig-14-caption",
"type": "caption",
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"source": "Fig. 14. Accuracy and deviation (I).",
"translation": "图 14 精度与偏差（I）。",
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{
"id": "fig-15-caption",
"type": "caption",
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"source_page": 10,
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"source": "Fig. 15. Accuracy and deviation (II).",
"translation": "图 15 精度与偏差（II）。",
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},
{
"id": "fig-16-caption",
"type": "caption",
"section": "第五节 实验研究",
"source_page": 10,
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"source": "Fig. 16. Algorithm running time.",
"translation": "图 16 算法运行时间。",
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{
"id": "sec5-023",
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"section": "第五节 实验研究",
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"source": "Fig. 14 and Fig. 15 visualize the inference accuracy averaged over time and the standard deviation upon the entire data stream. The standard deviation is calculated based on the inference accuracy of each time slot, representing the sensitivity to concept drifts and the stability of the algorithm [25]. Fig. 14 exhibits significantly better accuracy upon all four data streams and exhibits lower standard deviation compared to others on most data streams, indicating that our approach is less sensitive to concept drifts and is more stable. Fig. 15 exhibits that our algorithmic approach can work with different types of base models in the ensemble learning process. Different base models can be more preferred for different datasets.",
"translation": "图 14 与图 15 可视化了在整个数据流上对时间取平均的推理精度及其标准差。该标准差基于每个时隙的推理精度计算，代表对概念漂移的敏感程度以及算法的稳定性 [25]。图 14 显示出在全部四个数据流上都明显更好的精度，并且在大多数数据流上相比其他方法具有更低的标准差，说明我们的方法对概念漂移不那么敏感、也更稳定。图 15 显示出我们的算法方法在集成学习过程中能够与不同类型的基模型配合工作。对不同数据集而言，不同的基模型可能更受偏好。",
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"id": "sec5-024",
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"source": "Fig. 16 depicts the execution time of each algorithm in our approach. As the number of bidders reaches 64, Algorithms 1∼5 can complete in 0.73 seconds, 0.07 seconds, 20.30 seconds, 1.30 seconds, and 0.28 seconds for each auction, performing well compared to the length of a single time slot. This shows the computational efficiency of our approach in practice.",
"translation": "图 16 描绘了我们方法中每个算法的执行时间。当投标者数量达到 64 时，算法 1∼5 每场拍卖可分别在 0.73 秒、0.07 秒、20.30 秒、1.30 秒和 0.28 秒内完成，相对于单个时隙的长度而言表现良好。这表明我们的方法在实践中具有计算效率。",
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"id": "note-sec5-04",
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"section": "第五节 实验研究",
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"translation": "**为什么“便宜的差模型”值得单独讨论（承上启下）。** 本节实验的目标函数同时包含成本项与推理损失项，因此一个**报价很低、但推理很差的模型**在拍卖中可能因为便宜而被选中；它虽然降低了成本，却会抬高推理损失。图 8 与图 9 从机制性质（真实性、个体理性）的角度说明拍卖本身不会因这类模型而失效，图 12 至图 15 则考察模型更新与集成方法对精度和稳定性的影响。第六节 A 因此专门讨论如何权衡“便宜”与“推理差”，以及可以采用的过滤、修改算法、把推理损失并入拍卖目标等思路。",
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"section": "第五节 实验研究",
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"source_ids": [
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"source": "Fig. 17. Social cost under different time slot length.",
"translation": "图 17 不同时隙长度下的社会成本。",
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},
{
"id": "sec6-heading",
"type": "heading",
"section": "第六节 讨论",
"source_page": 11,
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"source": "VI. DISCUSSIONS",
"translation": "第六节 讨论",
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{
"id": "sec6-sub-a",
"type": "heading",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
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"source": "A. Cheap Models With Bad Inference Performance",
"translation": "A. 推理性能差的廉价模型",
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"id": "sec6-001",
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"section": "第六节 讨论",
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"zh-sec6-001"
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"source": "Our goal in this work is jointly optimizing the cost and the inference loss, as captured by the problem P0. It is yet crucial to manage the balance or trade-off between the cost and the inference performance of the models. One approach is to associate weights to the different terms in the objective function of P0. We leave to the service provider to decide the weight for each term in the objective function, depending on its own needs and requirements. In our current evaluations, the weights for the cost of the auctioneer, the cost of the bidders, and the inference loss in the objective are all set equal.",
"translation": "本工作的目标是联合优化成本与推理损失，这由问题 P0 刻画。然而，如何管理模型成本与推理性能之间的平衡或权衡至关重要。一种做法是为 P0 目标函数中的不同项赋予权重。我们把目标函数中每一项的权重交由服务提供方根据自身需要与要求来决定。在我们当前的评估中，目标函数中拍卖人的成本、投标者的成本以及推理损失这三项的权重都被设为相等。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec6-002",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-002"
],
"translation_ids": [
"zh-sec6-002"
],
"source": "Our strategy for solving P0 is decoupling the cost from the inference loss, and addressing the former first and the latter afterwards. With this strategy, we can already achieve multiple provable performance guarantees. In particular, Theorem 3 implies that at each time slot, as we update the weights for the models in the ensemble, the inference loss incurred by our model ensemble is no greater than a parameterized constant times the inference loss incurred by the single best model in terms of the inference loss in the ensemble at hindsight.",
"translation": "我们求解 P0 的策略是把成本与推理损失解耦，先处理前者、再处理后者。借助这一策略，我们已经能够获得多项可证明的性能保证。特别地，定理 3 表明：在每个时隙，随着我们更新集成中各模型的权重，我们的模型集成所产生的推理损失不超过“事后看来在集成中推理损失最小的单个最佳模型所产生的推理损失”的参数化常数倍。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec6-01",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"note-sec6-01"
],
"translation_ids": [
"zh-note-sec6-01"
],
"source": "",
"translation": "**这里“成本与推理性能的权衡”指的是什么。** 本文的目标函数同时包含拍卖人成本、投标者成本和推理损失三类项；由于存在**报价便宜但推理很差的模型**，压低成本与提高精度这两个目标会相互冲突。原文给出的处理方式是：
1）在目标函数中为不同项设置权重（权重值交给服务提供方自行决定，当前评估中三项等权）；
2）把成本与推理损失解耦，先解成本相关部分、后处理推理损失部分，从而保留本文已有的多项理论保证（如定理 3 给出的集成推理损失上界）。",
"notes": {
"kind": "green",
"origin": "source"
}
},
{
"id": "sec6-003",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-003"
],
"translation_ids": [
"zh-sec6-003"
],
"source": "There could be multiple methods to address the cheap models that have bad inference performance. First, an empirical method could be filtering out such models and ruling out such bids from participating in the auction before the auction starts. To do so, the system should allow the service provider to use a testing dataset to pre-check the performance of each model from the model providers. Second, a more systematic method could be based on modifying our algorithms in the manuscript without filtering out any bids in prior.",
"translation": "对于推理性能差的廉价模型，可以存在多种处理方法。第一，一种经验性方法是把这类模型过滤掉，并在拍卖开始之前排除这类投标参与拍卖。为此，系统应允许服务提供方使用一个测试数据集来预先检查来自各模型提供方的每个模型的性能。第二，一种更系统的方法可以基于修改本文中的算法，而不事先过滤掉任何投标。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec6-004",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-004"
],
"translation_ids": [
"zh-sec6-004"
],
"source": "To simultaneously consider cost and inference performance, we would want to modify our problem $\\mathcal{P}^t_3$, solved within Algorithm 4, by adding the inference loss to the objective and adding the constraints (1c)∼(1e). Solving this new $\\mathcal{P}^t_3$ faces new challenges: the data samples $M^t$ are unknown; the new $\\mathcal{P}^t_3$ now is a mixed-integer non-linear program, harder to solve; determining the weights for the models here may interfere with our current Algorithm 5; and Algorithm 4 that solves the new $\\mathcal{P}^t_3$ can impact our current Theorems 3 and 4.",
"translation": "为了同时考虑成本与推理性能，我们会希望修改算法 4 中所求解的问题 $\\mathcal{P}^t_3$，即把推理损失加入目标函数，并加入约束 (1c)∼(1e)。求解这个新的 $\\mathcal{P}^t_3$ 面临新的挑战：数据样本 $M^t$ 是未知的；新的 $\\mathcal{P}^t_3$ 现在是一个混合整数非线性规划，更难求解；此处为各模型确定权重可能会与我们当前的算法 5 相互干扰；而求解新 $\\mathcal{P}^t_3$ 的算法 4 又可能影响我们当前的定理 3 与定理 4。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec6-005",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-005"
],
"translation_ids": [
"zh-sec6-005"
],
"source": "Third, a new and different method could be incorporating the inference loss directly into the process of determining which bids to procure in each auction. This is non-trivial, and will raise the fundamental question of how to ensure truthfulness and individual rationality when part of the objective function for the auction is unknown, i.e., the inference loss is unknown as the data samples are unseen.",
"translation": "第三，一种新的、不同的方法可以是把推理损失直接纳入每场拍卖中确定采购哪些投标的过程。这并非易事，并且会引出一个根本性问题：当拍卖目标函数的一部分是未知的时候，即由于数据样本尚未见到而推理损失未知的时候，如何确保真实性与个体理性。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec6-sub-b",
"type": "heading",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-sub-b"
],
"translation_ids": [
"zh-sec6-sub-b"
],
"source": "B. Duration of Each Time Slot",
"translation": "B. 每个时隙的时长",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec6-006",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-006"
],
"translation_ids": [
"zh-sec6-006"
],
"source": "The time slots correspond to the decision frequency, depending on the system under control and the service provider. Our models, formulations, algorithms, and analysis consider the length of each time slot as pre-specified [76]. Yet, the length of the time slot or the frequency of the control decisions indeed impacts the social cost over time. We consider two cases as follows, both taking exactly the same inputs as P0.",
"translation": "时隙对应于决策频率，取决于所控制的系统以及服务提供方。我们的模型、形式化、算法与分析都把每个时隙的长度视为预先设定的 [76]。然而，时隙的长度或控制决策的频率确实会影响随时间累积的社会成本。我们考虑如下两种情形，二者的输入都与 P0 完全相同。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec6-007",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-007"
],
"translation_ids": [
"zh-sec6-007"
],
"source": "The first case is that every time slot t is divided into J smaller “time intervals” of equal length, which are indexed as $\\mathcal{J}=\\{1,2,\\ldots,J\\}$, and we make the control decisions for each time interval $j\\in\\mathcal{J}$ of each time slot t. The control decisions can thus be written as $x^{t,j}_n$, $y^{t,j}_n$, $z^{t,j}$, $\\alpha^{t,j}_{n,m}$, and $\\beta^{t,j}_m$. $M^{t,j}$ can represent the set of data samples that arrive at the time interval j of the time slot t, where $\\cup_{j=1}^{J}M^{t,j}=M^t$, $\\forall t$. Based on these, we can transform the problem P0 to the problem $P'_0$.",
"translation": "第一种情形是：把每个时隙 t 划分为 J 个等长的、更小的“时间区间”，它们以 $\\mathcal{J}=\\{1,2,\\ldots,J\\}$ 为索引，我们为每个时隙 t 的每个时间区间 $j\\in\\mathcal{J}$ 做出控制决策。于是控制决策可以写作 $x^{t,j}_n$、$y^{t,j}_n$、$z^{t,j}$、$\\alpha^{t,j}_{n,m}$ 和 $\\beta^{t,j}_m$。$M^{t,j}$ 可以表示在时隙 t 的时间区间 j 内到达的数据样本集合，其中 $\\cup_{j=1}^{J}M^{t,j}=M^t$，$\\forall t$。基于这些，我们可以把问题 P0 变换为问题 $P'_0$。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec6-008",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-008"
],
"translation_ids": [
"zh-sec6-008"
],
"source": "We also consider another problem $P''_0$, which is defined as $P'_0$ with the additional constraints that the bid selection and model hosting decisions for all the intervals within a time slot must stay unchanged (but are allowed to change across time slots). For the problems of P0, $P'_0$, and $P''_0$, we use P0, $P'_0$, and $P''_0$ to denote their objective functions, use the subscript OPT to denote the offline optimal objective value, and use $X^*$ to denote the offline optimal solution to P0. Then, we have",
"translation": "我们还考虑另一个问题 $P''_0$，它定义为在 $P'_0$ 之上附加如下约束：一个时隙内所有区间的投标选择与模型托管决策必须保持不变（但允许跨时隙变化）。对于 P0、$P'_0$ 与 $P''_0$ 这三个问题，我们用 P0、$P'_0$ 与 $P''_0$ 表示它们的目标函数，用下标 OPT 表示离线最优目标值，并用 $X^*$ 表示 P0 的离线最优解。于是我们有",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec6-009",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-009"
],
"translation_ids": [
"zh-sec6-009"
],
"source": "$P'_{0\\mathrm{OPT}}\\overset{(a)}{\\le}P''_{0\\mathrm{OPT}}\\overset{(b)}{\\le}P''_0(X^*)\\overset{(c)}{\\le}J\\cdot P_0(X^*)\\overset{(d)}{=}J\\cdot P_{0\\mathrm{OPT}}$.",
"translation": "$P'_{0\\mathrm{OPT}}\\overset{(a)}{\\le}P''_{0\\mathrm{OPT}}\\overset{(b)}{\\le}P''_0(X^*)\\overset{(c)}{\\le}J\\cdot P_0(X^*)\\overset{(d)}{=}J\\cdot P_{0\\mathrm{OPT}}$。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec6-010",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-010"
],
"translation_ids": [
"zh-sec6-010"
],
"source": "Inequality (a) holds, as $P'_0$ and $P''_0$ have the same objective function, but the latter has a more restricted solution space due to the additional constraints. Inequality (b) holds, because $P''_{0\\mathrm{OPT}}$ is the optimal value of $P''_0$. Also, note that $P''_0$ and P0 have exactly the same solution space. Inequality (c) holds for any feasible solution, if we just apply the additional constraints to the objective function $P''_0$. Equality (d) holds, due to the definition of $X^*$. Overall, the offline optimal social cost incurred by such per-time-interval fine-grained control is no greater than J times the offline optimal social cost incurred by the per-time-slot coarse-grained control.",
"translation": "不等式 (a) 成立，因为 $P'_0$ 与 $P''_0$ 具有相同的目标函数，但后者由于附加约束而具有更受限的解空间。不等式 (b) 成立，因为 $P''_{0\\mathrm{OPT}}$ 是 $P''_0$ 的最优值。另外注意，$P''_0$ 与 P0 具有完全相同的解空间。若我们只是把附加约束施加到目标函数 $P''_0$ 上，则不等式 (c) 对任意可行解都成立。等式 (d) 依据 $X^*$ 的定义成立。总体而言，这种按时间区间的细粒度控制所产生的离线最优社会成本，不超过按时隙的粗粒度控制所产生的离线最优社会成本的 J 倍。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec6-011",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-011"
],
"translation_ids": [
"zh-sec6-011"
],
"source": "The second case is that the entire time horizon is divided into J larger “time frames” of equal length, which are indexed by $\\mathcal{J}$, and each time slot uniquely belongs to a time frame, where the set of all the time slots of the time frame j can be represented as $T_j$; so, we make the control decisions for each time frame $j\\in\\mathcal{J}$. Note that in this case the corresponding version of the problem $P'_0$ can be equivalently defined as P0 with the additional constraints that the bid selection and model hosting decisions for all the time slots within a time frame must stay unchanged (but are allowed to change across time frames). It is obvious that $P'_{0\\mathrm{OPT}}\\ge P_{0\\mathrm{OPT}}$, as the former has a more restricted solution space. Overall, the offline optimal social cost incurred by such per-time-frame coarse-grained control is no less than the offline optimal social cost incurred by the per-time-slot fine-grained control.",
"translation": "第二种情形是：把整个时间范围划分为 J 个等长的、更大的“时间帧”，它们以 $\\mathcal{J}$ 为索引，每个时隙唯一地属于一个时间帧，其中时间帧 j 的所有时隙构成的集合可以表示为 $T_j$；于是我们为每个时间帧 $j\\in\\mathcal{J}$ 做出控制决策。注意，在此情形下，问题 $P'_0$ 的对应版本可以等价地定义为在 P0 之上附加如下约束：一个时间帧内所有时隙的投标选择与模型托管决策必须保持不变（但允许跨时间帧变化）。显然 $P'_{0\\mathrm{OPT}}\\ge P_{0\\mathrm{OPT}}$，因为前者的解空间更受限。总体而言，这种按时间帧的粗粒度控制所产生的离线最优社会成本，不低于按时隙的细粒度控制所产生的离线最优社会成本。",
"notes": {
"kind": null,
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}
},
{
"id": "sec6-012",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"sec6-012"
],
"translation_ids": [
"zh-sec6-012"
],
"source": "We have conducted new evaluations to investigate how the length of the time slot can impact the social cost incurred by our proposed approach in practice. For Fig. 17, we take the same inputs as our existing evaluations, with the same length of the entire time horizon, i.e., 100 minutes. Yet, we divide the time horizon into T = 50, 100, and 200 time slots, where the length of a single time slot is 2 minutes, 1 minute, and 0.5 minutes, respectively. We see that, as the time slot length increases, the total social cost increases, and that, as the time slot length decreases, the total social cost also decreases.",
"translation": "我们开展了新的评估，以考察时隙长度在实践中如何影响我们所提方法所产生的社会成本。对于图 17，我们采用与已有评估相同的输入，整个时间范围的长度也相同，即 100 分钟。但我们把时间范围划分为 T = 50、100 和 200 个时隙，其中单个时隙的长度分别为 2 分钟、1 分钟和 0.5 分钟。我们看到，随着时隙长度增大，总社会成本上升；而随着时隙长度减小，总社会成本也下降。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "note-sec6-02",
"type": "paragraph",
"section": "第六节 讨论",
"source_page": 11,
"source_ids": [
"note-sec6-02"
],
"translation_ids": [
"zh-note-sec6-02"
],
"source": "",
"translation": "**“时隙越细，社会成本越低”的直觉与形式化依据。** 原文用两个“解空间大小”的对比来解释：
• **情形一（更细）**：把每个时隙再切成 J 个等长时间区间，每个区间都可独立决策，记作 $P'_0$；若再要求一个时隙内所有区间的决策必须一致，则得到 $P''_0$。$P''_0$ 与 P0 的解空间相同，而把约束施加到目标上会放大 J 倍，于是得到链式不等式 $P'_{0\\mathrm{OPT}}\\le P''_{0\\mathrm{OPT}}\\le P''_0(X^*)\\le J\\cdot P_0(X^*)=J\\cdot P_{0\\mathrm{OPT}}$，即“细粒度控制的离线最优社会成本不超过按时隙粗粒度控制的离线最优社会成本的 J 倍”。
• **情形二（更粗）**：把整个时间范围切成 J 个更大的时间帧，要求一个时间帧内所有时隙的决策保持一致（$P'_0$ 的对应版本），解空间更受限，故 $P'_{0\\mathrm{OPT}}\\ge P_{0\\mathrm{OPT}}$。
原文并未给出这些不等式中的具体数值，只给出了“不小于/不大于 J 倍”这类序关系；图 17 中的经验结果（时隙为 2、1、0.5 分钟时总社会成本的相对高低）与上述方向一致。",
"notes": {
"kind": "blue",
"origin": "source"
}
},
{
"id": "sec7-heading",
"type": "heading",
"section": "第七节 相关工作",
"source_page": 11,
"source_ids": [
"sec7-heading"
],
"translation_ids": [
"zh-sec7-heading"
],
"source": "VII. RELATED WORK",
"translation": "第七节 相关工作",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec7-001",
"type": "paragraph",
"section": "第七节 相关工作",
"source_page": 11,
"source_ids": [
"sec7-001"
],
"translation_ids": [
"zh-sec7-001"
],
"source": "We categorize the previous research into three groups and highlight their drawbacks compared to our work, respectively. We also summarize and recap the uniqueness of our work.",
"translation": "我们把已有研究分为三类，并分别指出它们相对于本工作的不足。我们还总结并回顾了本工作的独特性。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec7-002",
"type": "paragraph",
"section": "第七节 相关工作",
"source_page": 11,
"source_ids": [
"sec7-002"
],
"translation_ids": [
"zh-sec7-002"
],
"source": "Ensemble Methods for Concept Drifts: Elwell and Polikar [21] trained a new classifier for each batch of data and used a dynamically-weighted majority-voting method to combine these classifiers. Jiao et al. [22] employed the K-nearest neighbors (KNN) method for dynamically selecting ensemble classifiers for each incoming data sample, and the final classification result is determined through a soft majority vote of multiple base classifiers. Zhao et al. [23] reused historical models for the ensemble and adaptively adjusted the weights for them. Liu et al. [24] utilized an instance-weighting method to adjust the sample weights and an ensemble diversity measure to select the classifiers. Sun et al. [25] exploited a diversity-based strategy to preserve the historical models. Lu et al. [26] trained individual classifiers by adaptively determining the data chunk size and the classifier weights.",
"translation": "面向概念漂移的集成方法：Elwell 与 Polikar [21] 为每一批数据训练一个新的分类器，并使用动态加权多数投票方法把这些分类器组合起来。Jiao 等人 [22] 采用 K 近邻（KNN）方法为每个到达的数据样本动态选择集成分类器，最终分类结果由多个基分类器的软多数投票决定。Zhao 等人 [23] 复用历史模型来构成集成，并自适应地调整它们的权重。Liu 等人 [24] 利用实例加权方法调整样本权重，并使用集成多样性度量来选择分类器。Sun 等人 [25] 利用基于多样性的策略来保存历史模型。Lu 等人 [26] 通过自适应地确定数据块大小与分类器权重来训练各个分类器。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec7-003",
"type": "paragraph",
"section": "第七节 相关工作",
"source_page": 12,
"source_ids": [
"sec7-003"
],
"translation_ids": [
"zh-sec7-003"
],
"source": "These works study various different ensemble approaches to tackle concept drifts; however, they only consider the inference loss without the system cost and overhead, and none of them has considered the cloud/edge environment.",
"translation": "这些工作研究了多种不同的集成方法来应对概念漂移；然而，它们只考虑推理损失，而没有考虑系统成本与开销，并且它们都没有考虑云/边缘环境。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec7-004",
"type": "paragraph",
"section": "第七节 相关工作",
"source_page": 12,
"source_ids": [
"sec7-004"
],
"translation_ids": [
"zh-sec7-004"
],
"source": "Ensemble Learning at Cloud/Edge: Yao et al. [27] built an ensemble of classifiers and combined the prediction results through majority voting in edge-assisted anomaly detection. Stephanie et al. [28] constructed ensembles via using local models to produce a generalized final model with high accuracy. Shlezinger et al. [29] proposed edge ensemble which enabling diverse predictors on each device to form a deep ensemble during the inference process. Bai et al. [30] built a deep neural network ensemble according to the features of admitted inference tasks to optimize the inference quality. Zhang et al. [31] adopted ensemble methods to improve the classification accuracy for meteorological applications in cloud/edge systems. Zong et al. [32] employed an ensemble of constituent caching policies for edge caching.",
"translation": "云/边缘环境中的集成学习：Yao 等人 [27] 在边缘辅助的异常检测中构建了分类器集成，并通过多数投票组合预测结果。Stephanie 等人 [28] 通过使用本地模型来构造集成，以产生具有高精度的泛化最终模型。Shlezinger 等人 [29] 提出了边缘集成（edge ensemble），使每台设备上的多样化预测器在推理过程中形成深度集成。Bai 等人 [30] 依据被接纳的推理任务的特征构建深度神经网络集成，以优化推理质量。Zhang 等人 [31] 在云/边缘系统中采用集成方法提升气象应用的分类精度。Zong 等人 [32] 把多种组成式缓存策略集成为一体用于边缘缓存。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec7-005",
"type": "paragraph",
"section": "第七节 相关工作",
"source_page": 12,
"source_ids": [
"sec7-005"
],
"translation_ids": [
"zh-sec7-005"
],
"source": "This line of research is often focused on an offline perspective, and does not typically consider the data streaming scenario in an online setting. None of them covers any incentive or market mechanism in the ensemble learning context.",
"translation": "这条研究路线往往着眼于离线视角，通常不考虑在线设定下的数据流场景。它们都没有在集成学习的语境下涉及任何激励机制或市场机制。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec7-006",
"type": "paragraph",
"section": "第七节 相关工作",
"source_page": 12,
"source_ids": [
"sec7-006"
],
"translation_ids": [
"zh-sec7-006"
],
"source": "AI Model Markets: Chen et al. [12] proposed the first formal framework for the ML model marketplace, employing a model-based pricing mechanism instead of data-based pricing. Weng et al. [33] deployed the marketplace on the blockchain and determined the model price based on the true performance. Sun et al. [34] adopted a distributed federated-learning-based marketplace with privacy and incentive considerations. Liu et al. [13] proposed an end-to-end marketplace and built compensation functions for data owners and price functions for buyers. Cao et al. [35] proposed an edge federated ML model marketplace with cost evaluation. Nguyen et al [36] designed a distributed model marketplace based on blockchain and considered the incentive mechanism in IoT networks.",
"translation": "AI 模型市场：Chen 等人 [12] 提出了机器学习模型市场的首个形式化框架，采用基于模型的定价机制而非基于数据的定价。Weng 等人 [33] 把市场部署在区块链上，并依据真实性能确定模型价格。Sun 等人 [34] 采用了一个考虑隐私与激励的、基于分布式联邦学习的市场。Liu 等人 [13] 提出了一个端到端的市场，并为数据所有者构建补偿函数、为买方构建价格函数。Cao 等人 [35] 提出了一个带成本评估的边缘联邦机器学习模型市场。Nguyen 等人 [36] 设计了一个基于区块链的分布式模型市场，并考虑了物联网网络中的激励机制。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec7-007",
"type": "paragraph",
"section": "第七节 相关工作",
"source_page": 12,
"source_ids": [
"sec7-007"
],
"translation_ids": [
"zh-sec7-007"
],
"source": "These works mainly adopt direct pricing, rather than auctions, without proving the economic properties as in our work. They also lack the consideration of the long-term constraints and the online setting that feature the problem we study.",
"translation": "这些工作主要采用直接定价而非拍卖，并且没有像我们工作中那样证明经济性质。它们也缺乏对我们所研究问题所具有的长期约束与在线设定的考虑。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec7-008",
"type": "paragraph",
"section": "第七节 相关工作",
"source_page": 12,
"source_ids": [
"sec7-008"
],
"translation_ids": [
"zh-sec7-008"
],
"source": "Overall, our research in this paper is different from works of the three groups as described above and is superior in the following aspects: (i) our mechanism consists of dynamic and repetitive auctions, capturing the long-term participation of bidders and achieving the desired economic properties in expectation; (ii) our mechanism works for unknown future inputs and streamed data in online settings, while controlling the state switching of model hosting in real time; and (iii) our mechanism adopts the model ensemble method to equip the service with robustness and stability against arbitrary concept drifts in the data streams in the cloud computing environment.",
"translation": "总体而言，本文的研究与上述三类工作都不同，并在以下方面更具优势：(i) 我们的机制由动态且重复的拍卖构成，能够刻画投标者的长期参与，并在期望意义下达成所期望的经济性质；(ii) 我们的机制适用于在线设定下未知的未来输入与流式数据，同时实时控制模型托管的状态切换；(iii) 我们的机制采用模型集成方法，使服务在云计算环境的数据流中面对任意概念漂移时具备鲁棒性与稳定性。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec8-heading",
"type": "heading",
"section": "第八节 结论",
"source_page": 12,
"source_ids": [
"sec8-heading"
],
"translation_ids": [
"zh-sec8-heading"
],
"source": "VIII. CONCLUSION",
"translation": "第八节 结论",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "sec8-001",
"type": "paragraph",
"section": "第八节 结论",
"source_page": 12,
"source_ids": [
"sec8-001"
],
"translation_ids": [
"zh-sec8-001"
],
"source": "Provisioning adaptive and accurate inference on streamed data is generally desired in a wide range of cloud services, yet gets largely overlooked in previous research. In this paper, we aim to bridge this gap. We take a unique perspective of acquiring models dynamically from the auction market and combining them with the service provider's own model to conduct ensemble learning. We design online algorithms with provable performance guarantees and economic properties to achieve the long-term optimization of system overhead and inference loss collectively for both the service provider and the model providers. We also conduct comprehensive and thorough evaluations with real-world and benchmark datasets under realistic settings to validate the performance of our approach from a variety of different angles. We hope our work could inspire more new research along this direction.",
"translation": "在流式数据上提供自适应且准确的推理，是各类云服务普遍期望具备的能力，但在以往研究中却在很大程度上被忽视了。本文旨在弥合这一空白。我们采取一个独特的视角：从拍卖市场中动态获取模型，并把它们与服务提供方自有的模型结合起来开展集成学习。我们设计了具有可证明性能保证与经济性质的在线算法，以对服务提供方与模型提供方二者共同实现系统开销与推理损失的长期优化。我们还在真实设定下使用真实世界数据集与基准数据集开展了全面而深入的评估，从多种不同角度验证我们方法的性能。我们希望本工作能够激发这一方向上更多的新研究。",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "ref-heading",
"type": "heading",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"ref-heading"
],
"translation_ids": [
"zh-ref-heading"
],
"source": "REFERENCES",
"translation": "参考文献",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "ref-note-policy",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"ref-note-policy"
],
"translation_ids": [
"zh-ref-note-policy"
],
"source": "",
"translation": "**本节处理政策（与正文译注分开）。** 参考文献保留原著录，不翻译题名，中文正文中的引用编号 [1]–[76] 与本节条目一一对应。中文学术写作惯例允许参考文献保持原文语种；逐条翻译 76 条题名会引入无法逐字核对的二次改写，且读者按编号检索时需要的是可对照的原始条目。因此这里呈现的就是原文著录本身。",
"notes": {
"kind": "green",
"origin": "source"
}
},
{
"id": "reference-01",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-01"
],
"translation_ids": [
"zh-reference-01"
],
"source": "[1] A. E. Eshratifar, M. S. Abrishami, and M. Pedram, “JointDNN: An efficient training and inference engine for intelligent mobile cloud computing services,” IEEE Trans. Mobile Comput., vol. 20, no. 2, pp. 565–576, Feb. 2021.",
"translation": "[1] A. E. Eshratifar, M. S. Abrishami, and M. Pedram, “JointDNN: An efficient training and inference engine for intelligent mobile cloud computing services,” IEEE Trans. Mobile Comput., vol. 20, no. 2, pp. 565–576, Feb. 2021.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-02",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-02"
],
"translation_ids": [
"zh-reference-02"
],
"source": "[2] J. Pan and J. McElhannon, “Future edge cloud and edge computing for Internet of Things applications,” IEEE Internet Things J., vol. 5, no. 1, pp. 439–449, Feb. 2018.",
"translation": "[2] J. Pan and J. McElhannon, “Future edge cloud and edge computing for Internet of Things applications,” IEEE Internet Things J., vol. 5, no. 1, pp. 439–449, Feb. 2018.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-03",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-03"
],
"translation_ids": [
"zh-reference-03"
],
"source": "[3] J. Gama, I. Žliobaite, A. Bifet, M. Pechenizkiy, and A. Bouchachia, “A ˙ survey on concept drift adaptation,” ACM Comput. Surv., vol. 46, no. 4, pp. 1–37, Apr. 2014.",
"translation": "[3] J. Gama, I. Žliobaite, A. Bifet, M. Pechenizkiy, and A. Bouchachia, “A ˙ survey on concept drift adaptation,” ACM Comput. Surv., vol. 46, no. 4, pp. 1–37, Apr. 2014.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-04",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-04"
],
"translation_ids": [
"zh-reference-04"
],
"source": "[4] J. Lu, A. Liu, F. Dong, F. Gu, J. Gama, and G. Zhang, “Learning under concept drift: A review,” IEEE Trans. Knowl. Data Eng., vol. 31, no. 12, pp. 2346–2363, Dec. 2018.",
"translation": "[4] J. Lu, A. Liu, F. Dong, F. Gu, J. Gama, and G. Zhang, “Learning under concept drift: A review,” IEEE Trans. Knowl. Data Eng., vol. 31, no. 12, pp. 2346–2363, Dec. 2018.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-05",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-05"
],
"translation_ids": [
"zh-reference-05"
],
"source": "[5] B. Krawczyk, L. L. Minku, J. Gama, J. Stefanowski, and M. Wozniak, “Ensemble learning for data stream analysis: A survey,” Inf. Fusion, vol. 37, pp. 132–156, Sep. 2017.",
"translation": "[5] B. Krawczyk, L. L. Minku, J. Gama, J. Stefanowski, and M. Wozniak, “Ensemble learning for data stream analysis: A survey,” Inf. Fusion, vol. 37, pp. 132–156, Sep. 2017.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-06",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-06"
],
"translation_ids": [
"zh-reference-06"
],
"source": "[6] H. M. Gomes, J. P. Barddal, F. Enembreck, and A. Bifet, “A survey on ensemble learning for data stream classification,” ACM Comput. Surv., vol. 50, no. 2, pp. 1–36, Mar. 2017.",
"translation": "[6] H. M. Gomes, J. P. Barddal, F. Enembreck, and A. Bifet, “A survey on ensemble learning for data stream classification,” ACM Comput. Surv., vol. 50, no. 2, pp. 1–36, Mar. 2017.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-07",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-07"
],
"translation_ids": [
"zh-reference-07"
],
"source": "[7] X. Dong, Z. Yu, W. Cao, Y. Shi, and Q. Ma, “A survey on ensemble learning,” Frontiers Comput. Sci., vol. 14, no. 2, pp. 241–258, Apr. 2020.",
"translation": "[7] X. Dong, Z. Yu, W. Cao, Y. Shi, and Q. Ma, “A survey on ensemble learning,” Frontiers Comput. Sci., vol. 14, no. 2, pp. 241–258, Apr. 2020.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-08",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-08"
],
"translation_ids": [
"zh-reference-08"
],
"source": "[8] Modzy. Accessed: 2024. [Online]. Available: https://www.modzy.com/",
"translation": "[8] Modzy. Accessed: 2024. [Online]. Available: https://www.modzy.com/",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-09",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-09"
],
"translation_ids": [
"zh-reference-09"
],
"source": "[9] Google Cloud Marketplace. Accessed: 2024. [Online]. Available: https://cloud.google.com/marketplace",
"translation": "[9] Google Cloud Marketplace. Accessed: 2024. [Online]. Available: https://cloud.google.com/marketplace",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-10",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-10"
],
"translation_ids": [
"zh-reference-10"
],
"source": "[10] AWS Marketplace. Accessed: 2024. [Online]. Available: https:// aws.amazon.com/marketplace/",
"translation": "[10] AWS Marketplace. Accessed: 2024. [Online]. Available: https:// aws.amazon.com/marketplace/",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-11",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-11"
],
"translation_ids": [
"zh-reference-11"
],
"source": "[11] Azure Marketplace. Accessed: 2024. [Online]. Available: https:// azuremarketplace.microsoft.com/zh-CN/",
"translation": "[11] Azure Marketplace. Accessed: 2024. [Online]. Available: https:// azuremarketplace.microsoft.com/zh-CN/",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-12",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-12"
],
"translation_ids": [
"zh-reference-12"
],
"source": "[12] L. Chen, P. Koutris, and A. Kumar, “Towards model-based pricing for machine learning in a data marketplace,” in Proc. SIGMOD, 2019, pp. 1535–1552.",
"translation": "[12] L. Chen, P. Koutris, and A. Kumar, “Towards model-based pricing for machine learning in a data marketplace,” in Proc. SIGMOD, 2019, pp. 1535–1552.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-13",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-13"
],
"translation_ids": [
"zh-reference-13"
],
"source": "[13] J. Liu, J. Lou, J. Liu, L. Xiong, J. Pei, and J. Sun, “Dealer: An end-toend model marketplace with differential privacy,” in Proc. VLDB, 2021, pp. 957–969. Authorized licensed use limited to: Northeastern University. Downloaded on May 21,2026 at 01:42:46 UTC from IEEE Xplore. Restrictions apply. ========== PAGE 13 ========== ZHANG et al.: TOWARD MARKET-ASSISTED AI: CLOUD INFERENCE FOR STREAMED DATA 805",
"translation": "[13] J. Liu, J. Lou, J. Liu, L. Xiong, J. Pei, and J. Sun, “Dealer: An end-toend model marketplace with differential privacy,” in Proc. VLDB, 2021, pp. 957–969. Authorized licensed use limited to: Northeastern University. Downloaded on May 21,2026 at 01:42:46 UTC from IEEE Xplore. Restrictions apply. ========== PAGE 13 ========== ZHANG et al.: TOWARD MARKET-ASSISTED AI: CLOUD INFERENCE FOR STREAMED DATA 805",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-14",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-14"
],
"translation_ids": [
"zh-reference-14"
],
"source": "[14] S. Chen, Z. Zhou, F. Liu, L. I. Zongpeng, and S. Ren, “CloudHeat: An efficient online market mechanism for datacenter heat harvesting,” ACM Trans. Model. Perform. Eval. Comput. Syst., vol. 3, no. 3, p. 11, 2018.",
"translation": "[14] S. Chen, Z. Zhou, F. Liu, L. I. Zongpeng, and S. Ren, “CloudHeat: An efficient online market mechanism for datacenter heat harvesting,” ACM Trans. Model. Perform. Eval. Comput. Syst., vol. 3, no. 3, p. 11, 2018.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-15",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-15"
],
"translation_ids": [
"zh-reference-15"
],
"source": "[15] S. Chen, L. Jiao, L. Wang, and F. Liu, “An online market mechanism for edge emergency demand response via cloudlet control,” in Proc. IEEE INFOCOM Conf. Comput. Commun., Apr. 2019, pp. 2566–2574.",
"translation": "[15] S. Chen, L. Jiao, L. Wang, and F. Liu, “An online market mechanism for edge emergency demand response via cloudlet control,” in Proc. IEEE INFOCOM Conf. Comput. Commun., Apr. 2019, pp. 2566–2574.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-16",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-16"
],
"translation_ids": [
"zh-reference-16"
],
"source": "[16] M. Derakhshan, D. M. Pennock, and A. Slivkins, “Beating greedy for approximating reserve prices in multi-unit VCG auctions,” in Proc. ACM-SIAM SODA, 2021, pp. 1099–1118.",
"translation": "[16] M. Derakhshan, D. M. Pennock, and A. Slivkins, “Beating greedy for approximating reserve prices in multi-unit VCG auctions,” in Proc. ACM-SIAM SODA, 2021, pp. 1099–1118.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-17",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-17"
],
"translation_ids": [
"zh-reference-17"
],
"source": "[17] L. Gao, F. Hou, and J. Huang, “Providing long-term participation incentive in participatory sensing,” in Proc. IEEE Conf. Comput. Commun. (INFOCOM), Apr. 2015, pp. 2803–2811.",
"translation": "[17] L. Gao, F. Hou, and J. Huang, “Providing long-term participation incentive in participatory sensing,” in Proc. IEEE Conf. Comput. Commun. (INFOCOM), Apr. 2015, pp. 2803–2811.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-18",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-18"
],
"translation_ids": [
"zh-reference-18"
],
"source": "[18] Y. Li, F. Li, S. Yang, P. Zhou, L. Zhu, and Y. Wang, “Three-stage Stackelberg long-term incentive mechanism and monetization for mobile crowdsensing: An Online learning approach,” IEEE Trans. Netw. Sci. Eng., vol. 8, no. 2, pp. 1385–1398, Apr./Jun. 2021.",
"translation": "[18] Y. Li, F. Li, S. Yang, P. Zhou, L. Zhu, and Y. Wang, “Three-stage Stackelberg long-term incentive mechanism and monetization for mobile crowdsensing: An Online learning approach,” IEEE Trans. Netw. Sci. Eng., vol. 8, no. 2, pp. 1385–1398, Apr./Jun. 2021.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-19",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-19"
],
"translation_ids": [
"zh-reference-19"
],
"source": "[19] F. Li, J. Liu, and B. Ji, “Combinatorial sleeping bandits with fairness constraints,” IEEE Trans. Netw. Sci. Eng., vol. 7, no. 3, pp. 1799–1813, Jul. 2020.",
"translation": "[19] F. Li, J. Liu, and B. Ji, “Combinatorial sleeping bandits with fairness constraints,” IEEE Trans. Netw. Sci. Eng., vol. 7, no. 3, pp. 1799–1813, Jul. 2020.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-20",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-20"
],
"translation_ids": [
"zh-reference-20"
],
"source": "[20] Z. Wang, L. Gao, and J. Huang, “Socially-optimal mechanism design for incentivized online learning,” in Proc. IEEE INFOCOM Conf. Comput. Commun., May 2022, pp. 1828–1837.",
"translation": "[20] Z. Wang, L. Gao, and J. Huang, “Socially-optimal mechanism design for incentivized online learning,” in Proc. IEEE INFOCOM Conf. Comput. Commun., May 2022, pp. 1828–1837.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-21",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-21"
],
"translation_ids": [
"zh-reference-21"
],
"source": "[21] R. Elwell and R. Polikar, “Incremental learning of concept drift in nonstationary environments,” IEEE Trans. Neural Netw., vol. 22, no. 10, pp. 1517–1531, Oct. 2011.",
"translation": "[21] R. Elwell and R. Polikar, “Incremental learning of concept drift in nonstationary environments,” IEEE Trans. Neural Netw., vol. 22, no. 10, pp. 1517–1531, Oct. 2011.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-22",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-22"
],
"translation_ids": [
"zh-reference-22"
],
"source": "[22] B. Jiao, Y. Guo, D. Gong, and Q. Chen, “Dynamic ensemble selection for imbalanced data streams with concept drift,” IEEE Trans. Neural Netw. Learn. Syst., vol. 35, no. 1, pp. 1278–1291, Jun. 2022.",
"translation": "[22] B. Jiao, Y. Guo, D. Gong, and Q. Chen, “Dynamic ensemble selection for imbalanced data streams with concept drift,” IEEE Trans. Neural Netw. Learn. Syst., vol. 35, no. 1, pp. 1278–1291, Jun. 2022.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-23",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-23"
],
"translation_ids": [
"zh-reference-23"
],
"source": "[23] P. Zhao, L.-W. Cai, and Z.-H. Zhou, “Handling concept drift via model reuse,” Mach. Learn., vol. 109, no. 3, pp. 533–568, Mar. 2020.",
"translation": "[23] P. Zhao, L.-W. Cai, and Z.-H. Zhou, “Handling concept drift via model reuse,” Mach. Learn., vol. 109, no. 3, pp. 533–568, Mar. 2020.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-24",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-24"
],
"translation_ids": [
"zh-reference-24"
],
"source": "[24] A. Liu, J. Lu, and G. Zhang, “Diverse instance-weighting ensemble based on region drift disagreement for concept drift adaptation,” IEEE Trans. Neural Netw. Learn. Syst., vol. 32, no. 1, pp. 293–307, Jan. 2021.",
"translation": "[24] A. Liu, J. Lu, and G. Zhang, “Diverse instance-weighting ensemble based on region drift disagreement for concept drift adaptation,” IEEE Trans. Neural Netw. Learn. Syst., vol. 32, no. 1, pp. 293–307, Jan. 2021.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-25",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-25"
],
"translation_ids": [
"zh-reference-25"
],
"source": "[25] Y. Sun, K. Tang, Z. Zhu, and X. Yao, “Concept drift adaptation by exploiting historical knowledge,” IEEE Trans. Neural Netw. Learn. Syst., vol. 29, no. 10, pp. 4822–4832, Oct. 2018.",
"translation": "[25] Y. Sun, K. Tang, Z. Zhu, and X. Yao, “Concept drift adaptation by exploiting historical knowledge,” IEEE Trans. Neural Netw. Learn. Syst., vol. 29, no. 10, pp. 4822–4832, Oct. 2018.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-26",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-26"
],
"translation_ids": [
"zh-reference-26"
],
"source": "[26] Y. Lu, Y.-M. Cheung, and Y. Yan Tang, “Adaptive chunk-based dynamic weighted majority for imbalanced data streams with concept drift,” IEEE Trans. Neural Netw. Learn. Syst., vol. 31, no. 8, pp. 2764–2778, Aug. 2020.",
"translation": "[26] Y. Lu, Y.-M. Cheung, and Y. Yan Tang, “Adaptive chunk-based dynamic weighted majority for imbalanced data streams with concept drift,” IEEE Trans. Neural Netw. Learn. Syst., vol. 31, no. 8, pp. 2764–2778, Aug. 2020.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-27",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-27"
],
"translation_ids": [
"zh-reference-27"
],
"source": "[27] W. Yao, K. Zhang, C. Yu, and H. Zhao, “Exploiting ensemble learning for edge-assisted anomaly detection scheme in e-healthcare system,” in Proc. IEEE Global Commun. Conf. (GLOBECOM), Dec. 2021, pp. 1–7.",
"translation": "[27] W. Yao, K. Zhang, C. Yu, and H. Zhao, “Exploiting ensemble learning for edge-assisted anomaly detection scheme in e-healthcare system,” in Proc. IEEE Global Commun. Conf. (GLOBECOM), Dec. 2021, pp. 1–7.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-28",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-28"
],
"translation_ids": [
"zh-reference-28"
],
"source": "[28] V. Stephanie, I. Khalil, M. S. Rahman, and M. Atiquzzaman, “Privacypreserving ensemble infused enhanced deep neural network framework for edge cloud convergence,” IEEE Internet Things J., vol. 10, no. 5, pp. 3763–3773, Mar. 2023.",
"translation": "[28] V. Stephanie, I. Khalil, M. S. Rahman, and M. Atiquzzaman, “Privacypreserving ensemble infused enhanced deep neural network framework for edge cloud convergence,” IEEE Internet Things J., vol. 10, no. 5, pp. 3763–3773, Mar. 2023.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-29",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-29"
],
"translation_ids": [
"zh-reference-29"
],
"source": "[29] N. Shlezinger, E. Farhan, H. Morgenstern, and Y. C. Eldar, “Collaborative inference via ensembles on the edge,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Jun. 2021, pp. 8478–8482.",
"translation": "[29] N. Shlezinger, E. Farhan, H. Morgenstern, and Y. C. Eldar, “Collaborative inference via ensembles on the edge,” in Proc. IEEE Int. Conf. Acoust., Speech Signal Process. (ICASSP), Jun. 2021, pp. 8478–8482.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-30",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-30"
],
"translation_ids": [
"zh-reference-30"
],
"source": "[30] Y. Bai, L. Chen, M. Abdel-Mottaleb, and J. Xu, “Automated ensemble for deep learning inference on edge computing platforms,” IEEE Internet Things J., vol. 9, no. 6, pp. 4202–4213, Mar. 2022.",
"translation": "[30] Y. Bai, L. Chen, M. Abdel-Mottaleb, and J. Xu, “Automated ensemble for deep learning inference on edge computing platforms,” IEEE Internet Things J., vol. 9, no. 6, pp. 4202–4213, Mar. 2022.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-31",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-31"
],
"translation_ids": [
"zh-reference-31"
],
"source": "[31] J. Zhang, P. Liu, F. Zhang, H. Iwabuchi, A. A. d. H. e. A. de Moura, and V. H. C. de Albuquerque, “Ensemble meteorological cloud classification meets Internet of dependable and controllable things,” IEEE Internet Things J., vol. 8, no. 5, pp. 3323–3330, Mar. 2021.",
"translation": "[31] J. Zhang, P. Liu, F. Zhang, H. Iwabuchi, A. A. d. H. e. A. de Moura, and V. H. C. de Albuquerque, “Ensemble meteorological cloud classification meets Internet of dependable and controllable things,” IEEE Internet Things J., vol. 8, no. 5, pp. 3323–3330, Mar. 2021.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-32",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-32"
],
"translation_ids": [
"zh-reference-32"
],
"source": "[32] T. Zong, C. Li, Y. Lei, G. Li, H. Cao, and Y. Liu, “Cocktail edge caching: Ride dynamic trends of content popularity with ensemble learning,” IEEE/ACM Trans. Netw., vol. 31, no. 1, pp. 208–219, Feb. 2023.",
"translation": "[32] T. Zong, C. Li, Y. Lei, G. Li, H. Cao, and Y. Liu, “Cocktail edge caching: Ride dynamic trends of content popularity with ensemble learning,” IEEE/ACM Trans. Netw., vol. 31, no. 1, pp. 208–219, Feb. 2023.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-33",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-33"
],
"translation_ids": [
"zh-reference-33"
],
"source": "[33] J. Weng, J. Weng, C. Cai, H. Huang, and C. Wang, “Golden grain: Building a secure and decentralized model marketplace for MLaaS,” IEEE Trans. Depend. Secure Comput., vol. 19, no. 5, pp. 3149–3167, Sep. 2022.",
"translation": "[33] J. Weng, J. Weng, C. Cai, H. Huang, and C. Wang, “Golden grain: Building a secure and decentralized model marketplace for MLaaS,” IEEE Trans. Depend. Secure Comput., vol. 19, no. 5, pp. 3149–3167, Sep. 2022.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-34",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-34"
],
"translation_ids": [
"zh-reference-34"
],
"source": "[34] P. Sun, X. Chen, G. Liao, and J. Huang, “A profit-maximizing model marketplace with differentially private federated learning,” in Proc. IEEE INFOCOM Conf. Comput. Commun., May 2022, pp. 1439–1448.",
"translation": "[34] P. Sun, X. Chen, G. Liao, and J. Huang, “A profit-maximizing model marketplace with differentially private federated learning,” in Proc. IEEE INFOCOM Conf. Comput. Commun., May 2022, pp. 1439–1448.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-35",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-35"
],
"translation_ids": [
"zh-reference-35"
],
"source": "[35] T.-D. Cao, H.-L. Truong, T. Truong-Huu, and M.-T. Nguyen, “Enabling awareness of quality of training and costs in federated machine learning marketplaces,” in Proc. IEEE/ACM 15th Int. Conf. Utility Cloud Comput. (UCC), Dec. 2022, pp. 41–50.",
"translation": "[35] T.-D. Cao, H.-L. Truong, T. Truong-Huu, and M.-T. Nguyen, “Enabling awareness of quality of training and costs in federated machine learning marketplaces,” in Proc. IEEE/ACM 15th Int. Conf. Utility Cloud Comput. (UCC), Dec. 2022, pp. 41–50.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-36",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-36"
],
"translation_ids": [
"zh-reference-36"
],
"source": "[36] L. D. Nguyen, S. R. Pandey, S. Beatriz, A. Broering, and P. Popovski, “A marketplace for trading AI models based on blockchain and incentives for IoT data,” 2021, arXiv:2112.02870.",
"translation": "[36] L. D. Nguyen, S. R. Pandey, S. Beatriz, A. Broering, and P. Popovski, “A marketplace for trading AI models based on blockchain and incentives for IoT data,” 2021, arXiv:2112.02870.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-37",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-37"
],
"translation_ids": [
"zh-reference-37"
],
"source": "[37] E. C. Hall and R. M. Willett, “Online convex optimization in dynamic environments,” IEEE J. Sel. Topics Signal Process., vol. 9, no. 4, pp. 647–662, Jun. 2015.",
"translation": "[37] E. C. Hall and R. M. Willett, “Online convex optimization in dynamic environments,” IEEE J. Sel. Topics Signal Process., vol. 9, no. 4, pp. 647–662, Jun. 2015.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-38",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-38"
],
"translation_ids": [
"zh-reference-38"
],
"source": "[38] T. Chen, Q. Ling, and G. B. Giannakis, “An online convex optimization approach to proactive network resource allocation,” IEEE Trans. Signal Process., vol. 65, no. 24, pp. 6350–6364, Dec. 2017.",
"translation": "[38] T. Chen, Q. Ling, and G. B. Giannakis, “An online convex optimization approach to proactive network resource allocation,” IEEE Trans. Signal Process., vol. 65, no. 24, pp. 6350–6364, Dec. 2017.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-39",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-39"
],
"translation_ids": [
"zh-reference-39"
],
"source": "[39] N. Cesa-Bianchi and G. Lugosi, Prediction, Learning, and Games. Cambridge, U.K.: Cambridge Univ. Press, 2006.",
"translation": "[39] N. Cesa-Bianchi and G. Lugosi, Prediction, Learning, and Games. Cambridge, U.K.: Cambridge Univ. Press, 2006.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-40",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-40"
],
"translation_ids": [
"zh-reference-40"
],
"source": "[40] T. Chen and G. B. Giannakis, “Bandit convex optimization for scalable and dynamic IoT management,” IEEE Internet Things J., vol. 6, no. 1, pp. 1276–1286, Feb. 2019.",
"translation": "[40] T. Chen and G. B. Giannakis, “Bandit convex optimization for scalable and dynamic IoT management,” IEEE Internet Things J., vol. 6, no. 1, pp. 1276–1286, Feb. 2019.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-41",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-41"
],
"translation_ids": [
"zh-reference-41"
],
"source": "[41] V. Losing, B. Hammer, and H. Wersing, “KNN classifier with self adjusting memory for heterogeneous concept drift,” in Proc. IEEE 16th Int. Conf. Data Mining (ICDM), Dec. 2016, pp. 291–300.",
"translation": "[41] V. Losing, B. Hammer, and H. Wersing, “KNN classifier with self adjusting memory for heterogeneous concept drift,” in Proc. IEEE 16th Int. Conf. Data Mining (ICDM), Dec. 2016, pp. 291–300.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-42",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-42"
],
"translation_ids": [
"zh-reference-42"
],
"source": "[42] D. M. dos Reis, P. Flach, S. Matwin, and G. Batista, “Fast unsupervised online drift detection using incremental Kolmogorov–Smirnov test,” in Proc. 22nd ACM SIGKDD Int. Conf. Knowl. Discovery Data Mining, Aug. 2016, pp. 1545–1554.",
"translation": "[42] D. M. dos Reis, P. Flach, S. Matwin, and G. Batista, “Fast unsupervised online drift detection using incremental Kolmogorov–Smirnov test,” in Proc. 22nd ACM SIGKDD Int. Conf. Knowl. Discovery Data Mining, Aug. 2016, pp. 1545–1554.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-43",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-43"
],
"translation_ids": [
"zh-reference-43"
],
"source": "[43] I. Katakis, G. Tsoumakas, E. Banos, N. Bassiliades, and I. Vlahavas, “An adaptive personalized news dissemination system,” J. Intell. Inf. Syst., vol. 32, no. 2, pp. 191–212, Apr. 2009.",
"translation": "[43] I. Katakis, G. Tsoumakas, E. Banos, N. Bassiliades, and I. Vlahavas, “An adaptive personalized news dissemination system,” J. Intell. Inf. Syst., vol. 32, no. 2, pp. 191–212, Apr. 2009.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-44",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-44"
],
"translation_ids": [
"zh-reference-44"
],
"source": "[44] M. Harries, “Splice-2 comparative evaluation: Electricity pricing,” Artif. Intell. Group, School Comput. Sci. Eng., Univ. New South Wales, Sydney, NSW, Australia, Tech. Rep. UNSW-CSE-TR-9905, 1999.",
"translation": "[44] M. Harries, “Splice-2 comparative evaluation: Electricity pricing,” Artif. Intell. Group, School Comput. Sci. Eng., Univ. New South Wales, Sydney, NSW, Australia, Tech. Rep. UNSW-CSE-TR-9905, 1999.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-45",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-45"
],
"translation_ids": [
"zh-reference-45"
],
"source": "[45] Alibaba Cloud. Accessed: 2024. [Online]. Available: https://www. aliyun.com/",
"translation": "[45] Alibaba Cloud. Accessed: 2024. [Online]. Available: https://www. aliyun.com/",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-46",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-46"
],
"translation_ids": [
"zh-reference-46"
],
"source": "[46] Alibaba Cloud Server Geographical and Availability Zone Distribution List. Accessed: 2024. [Online]. Available: https://www.aliyunfuwuqi. com/region/3796/",
"translation": "[46] Alibaba Cloud Server Geographical and Availability Zone Distribution List. Accessed: 2024. [Online]. Available: https://www.aliyunfuwuqi. com/region/3796/",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-47",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-47"
],
"translation_ids": [
"zh-reference-47"
],
"source": "[47] Hourly Pricing. Accessed: 2024. [Online]. Available: https://hourly pricing.comed.com/live-prices/",
"translation": "[47] Hourly Pricing. Accessed: 2024. [Online]. Available: https://hourly pricing.comed.com/live-prices/",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-48",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-48"
],
"translation_ids": [
"zh-reference-48"
],
"source": "[48] E. Strubell, A. Ganesh, and A. McCallum, “Energy and policy considerations for deep learning in NLP,” 2019, arXiv:1906.02243.",
"translation": "[48] E. Strubell, A. Ganesh, and A. McCallum, “Energy and policy considerations for deep learning in NLP,” 2019, arXiv:1906.02243.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-49",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-49"
],
"translation_ids": [
"zh-reference-49"
],
"source": "[49] X. Zhao et al., “DEAR: Deep reinforcement learning for online advertising impression in recommender systems,” in Proc. AAAI, 2021, pp. 750–758.",
"translation": "[49] X. Zhao et al., “DEAR: Deep reinforcement learning for online advertising impression in recommender systems,” in Proc. AAAI, 2021, pp. 750–758.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-50",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-50"
],
"translation_ids": [
"zh-reference-50"
],
"source": "[50] H. Zhu et al., “Learning tree-based deep model for recommender systems,” in Proc. 24th ACM SIGKDD Int. Conf. Knowl. Discovery Data Mining, Jul. 2018, pp. 1079–1088.",
"translation": "[50] H. Zhu et al., “Learning tree-based deep model for recommender systems,” in Proc. 24th ACM SIGKDD Int. Conf. Knowl. Discovery Data Mining, Jul. 2018, pp. 1079–1088.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-51",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-51"
],
"translation_ids": [
"zh-reference-51"
],
"source": "[51] A. Hard et al., “Federated learning for mobile keyboard prediction,” 2018, arXiv:1811.03604.",
"translation": "[51] A. Hard et al., “Federated learning for mobile keyboard prediction,” 2018, arXiv:1811.03604.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-52",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-52"
],
"translation_ids": [
"zh-reference-52"
],
"source": "[52] F. Orabona, “A modern introduction to online learning,” 2019, arXiv:1912.13213.",
"translation": "[52] F. Orabona, “A modern introduction to online learning,” 2019, arXiv:1912.13213.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-53",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-53"
],
"translation_ids": [
"zh-reference-53"
],
"source": "[53] S. Shalev-Shwartz, “Online learning and online convex optimization,” Found. Trends Mach. Learn., vol. 4, no. 2, pp. 107–194, 2012.",
"translation": "[53] S. Shalev-Shwartz, “Online learning and online convex optimization,” Found. Trends Mach. Learn., vol. 4, no. 2, pp. 107–194, 2012.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-54",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-54"
],
"translation_ids": [
"zh-reference-54"
],
"source": "[54] X. Wei, H. Yu, and M. J. Neely, “Online primal-dual mirror descent under stochastic constraints,” Proc. ACM Meas. Anal. Comput. Syst., vol. 4, no. 2, pp. 1–36, 2020.",
"translation": "[54] X. Wei, H. Yu, and M. J. Neely, “Online primal-dual mirror descent under stochastic constraints,” Proc. ACM Meas. Anal. Comput. Syst., vol. 4, no. 2, pp. 1–36, 2020.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-55",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-55"
],
"translation_ids": [
"zh-reference-55"
],
"source": "[55] S. Balseiro, H. Lu, and V. Mirrokni, “Dual mirror descent for online allocation problems,” in Proc. ICML, 2020, pp. 613–628.",
"translation": "[55] S. Balseiro, H. Lu, and V. Mirrokni, “Dual mirror descent for online allocation problems,” in Proc. ICML, 2020, pp. 613–628.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-56",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-56"
],
"translation_ids": [
"zh-reference-56"
],
"source": "[56] A. Lobos, P. Grigas, and Z. Wen, “Joint online learning and decisionmaking via dual mirror descent,” in Proc. ICML, 2021, pp. 7080–7089.",
"translation": "[56] A. Lobos, P. Grigas, and Z. Wen, “Joint online learning and decisionmaking via dual mirror descent,” in Proc. ICML, 2021, pp. 7080–7089.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-57",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-57"
],
"translation_ids": [
"zh-reference-57"
],
"source": "[57] N. Eshraghi and B. Liang, “Improving dynamic regret in distributed online mirror descent using primal and dual information,” in Proc. LDCC, 2022, pp. 637–649.",
"translation": "[57] N. Eshraghi and B. Liang, “Improving dynamic regret in distributed online mirror descent using primal and dual information,” in Proc. LDCC, 2022, pp. 637–649.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-58",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-58"
],
"translation_ids": [
"zh-reference-58"
],
"source": "[58] S. Shahrampour and A. Jadbabaie, “Distributed online optimization in dynamic environments using mirror descent,” IEEE Trans. Autom. Control, vol. 63, no. 3, pp. 714–725, Mar. 2018.",
"translation": "[58] S. Shahrampour and A. Jadbabaie, “Distributed online optimization in dynamic environments using mirror descent,” IEEE Trans. Autom. Control, vol. 63, no. 3, pp. 714–725, Mar. 2018.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-59",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-59"
],
"translation_ids": [
"zh-reference-59"
],
"source": "[59] S. Chen, Y.-J. Zhang, W.-W. Tu, P. Zhao, and L. Zhang, “Optimistic online mirror descent for bridging stochastic and adversarial online convex optimization,” J. Mach. Learn. Res., vol. 25, no. 178, pp. 1–62, 2024.",
"translation": "[59] S. Chen, Y.-J. Zhang, W.-W. Tu, P. Zhao, and L. Zhang, “Optimistic online mirror descent for bridging stochastic and adversarial online convex optimization,” J. Mach. Learn. Res., vol. 25, no. 178, pp. 1–62, 2024.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-60",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-60"
],
"translation_ids": [
"zh-reference-60"
],
"source": "[60] N. Eshraghi and B. Liang, “Dynamic regret of online mirror descent for relatively smooth convex cost functions,” IEEE Control Syst. Lett., vol. 6, pp. 2395–2400, 2022.",
"translation": "[60] N. Eshraghi and B. Liang, “Dynamic regret of online mirror descent for relatively smooth convex cost functions,” IEEE Control Syst. Lett., vol. 6, pp. 2395–2400, 2022.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-61",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-61"
],
"translation_ids": [
"zh-reference-61"
],
"source": "[61] H. Yu and M. J. Neely, “A low complexity algorithm with o( √ t) regret and o(1) constraint violations for online convex optimization with long term constraints,” J. Mach. Learn. Res., vol. 21, no. 1, pp. 1–24, 2020.",
"translation": "[61] H. Yu and M. J. Neely, “A low complexity algorithm with o( √ t) regret and o(1) constraint violations for online convex optimization with long term constraints,” J. Mach. Learn. Res., vol. 21, no. 1, pp. 1–24, 2020.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-62",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-62"
],
"translation_ids": [
"zh-reference-62"
],
"source": "[62] J. Yuan and A. Lamperski, “Online convex optimization for cumulative constraints,” in Proc. Adv. Neural Inf. Process. Syst., vol. 31, 2018, pp. 6137–6146.",
"translation": "[62] J. Yuan and A. Lamperski, “Online convex optimization for cumulative constraints,” in Proc. Adv. Neural Inf. Process. Syst., vol. 31, 2018, pp. 6137–6146.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-63",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-63"
],
"translation_ids": [
"zh-reference-63"
],
"source": "[63] H. Yu, M. Neely, and X. Wei, “Online convex optimization with stochastic constraints,” in Proc. Adv. Neural Inf. Process. Syst., vol. 30, 2017, pp. 1428–1438. Authorized licensed use limited to: Northeastern University. Downloaded on May 21,2026 at 01:42:46 UTC from IEEE Xplore. Restrictions apply. ========== PAGE 14 ========== 806 IEEE TRANSACTIONS ON NETWORKING, VOL. 33, NO. 2, APRIL 2025",
"translation": "[63] H. Yu, M. Neely, and X. Wei, “Online convex optimization with stochastic constraints,” in Proc. Adv. Neural Inf. Process. Syst., vol. 30, 2017, pp. 1428–1438. Authorized licensed use limited to: Northeastern University. Downloaded on May 21,2026 at 01:42:46 UTC from IEEE Xplore. Restrictions apply. ========== PAGE 14 ========== 806 IEEE TRANSACTIONS ON NETWORKING, VOL. 33, NO. 2, APRIL 2025",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-64",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-64"
],
"translation_ids": [
"zh-reference-64"
],
"source": "[64] M. Mahdavi, R. Jin, and T. Yang, “Trading regret for efficiency: Online convex optimization with long term constraints,” J. Mach. Learn. Res., vol. 13, no. 1, pp. 2503–2528, 2012.",
"translation": "[64] M. Mahdavi, R. Jin, and T. Yang, “Trading regret for efficiency: Online convex optimization with long term constraints,” J. Mach. Learn. Res., vol. 13, no. 1, pp. 2503–2528, 2012.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-65",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-65"
],
"translation_ids": [
"zh-reference-65"
],
"source": "[65] X. Yi et al., “Distributed online convex optimization with adversarial constraints: Reduced cumulative constraint violation bounds under Slater’s condition,” 2023, arXiv:2306.00149.",
"translation": "[65] X. Yi et al., “Distributed online convex optimization with adversarial constraints: Reduced cumulative constraint violation bounds under Slater’s condition,” 2023, arXiv:2306.00149.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-66",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-66"
],
"translation_ids": [
"zh-reference-66"
],
"source": "[66] A. Sinha and R. Vaze, “Optimal algorithms for online convex optimization with adversarial constraints,” 2023, arXiv:2310.18955.",
"translation": "[66] A. Sinha and R. Vaze, “Optimal algorithms for online convex optimization with adversarial constraints,” 2023, arXiv:2310.18955.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-67",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-67"
],
"translation_ids": [
"zh-reference-67"
],
"source": "[67] A. Sinha and R. Vaze, “Tight bounds for online convex optimization with adversarial constraints,” 2024, arXiv:2405.09296.",
"translation": "[67] A. Sinha and R. Vaze, “Tight bounds for online convex optimization with adversarial constraints,” 2024, arXiv:2405.09296.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-68",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-68"
],
"translation_ids": [
"zh-reference-68"
],
"source": "[68] S. Paternain, S. Lee, M. M. Zavlanos, and A. Ribeiro, “Distributed constrained online learning,” IEEE Trans. Signal Process., vol. 68, pp. 3486–3499, 2020.",
"translation": "[68] S. Paternain, S. Lee, M. M. Zavlanos, and A. Ribeiro, “Distributed constrained online learning,” IEEE Trans. Signal Process., vol. 68, pp. 3486–3499, 2020.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-69",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-69"
],
"translation_ids": [
"zh-reference-69"
],
"source": "[69] S. Mizuno and F. Jarre, “Global and polynomial-time convergence of an infeasible-interior-point algorithm using inexact computation,” Math. Program., vol. 84, no. 1, pp. 105–122, Jan. 1999.",
"translation": "[69] S. Mizuno and F. Jarre, “Global and polynomial-time convergence of an infeasible-interior-point algorithm using inexact computation,” Math. Program., vol. 84, no. 1, pp. 105–122, Jan. 1999.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-70",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-70"
],
"translation_ids": [
"zh-reference-70"
],
"source": "[70] R. Gandhi, S. Khuller, S. Parthasarathy, and A. Srinivasan, “Dependent rounding and its applications to approximation algorithms,” J. ACM, vol. 53, no. 3, pp. 324–360, 2006.",
"translation": "[70] R. Gandhi, S. Khuller, S. Parthasarathy, and A. Srinivasan, “Dependent rounding and its applications to approximation algorithms,” J. ACM, vol. 53, no. 3, pp. 324–360, 2006.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-71",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-71"
],
"translation_ids": [
"zh-reference-71"
],
"source": "[71] A. Archer and E. Tardos, “Truthful mechanisms for one-parameter agents,” in Proc. 42nd IEEE Symp. Found. Comput. Sci., Oct. 2001, pp. 482–491.",
"translation": "[71] A. Archer and E. Tardos, “Truthful mechanisms for one-parameter agents,” in Proc. 42nd IEEE Symp. Found. Comput. Sci., Oct. 2001, pp. 482–491.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-72",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-72"
],
"translation_ids": [
"zh-reference-72"
],
"source": "[72] B. H. Korte, J. Vygen, B. Korte, and J. Vygen, Combinatorial Optimization. Cham, Switzerland: Springer, 2011.",
"translation": "[72] B. H. Korte, J. Vygen, B. Korte, and J. Vygen, Combinatorial Optimization. Cham, Switzerland: Springer, 2011.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-73",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-73"
],
"translation_ids": [
"zh-reference-73"
],
"source": "[73] L. Breiman, Classification Regression Trees. Evanston, IL, USA: Routledge, 2017.",
"translation": "[73] L. Breiman, Classification Regression Trees. Evanston, IL, USA: Routledge, 2017.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-74",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-74"
],
"translation_ids": [
"zh-reference-74"
],
"source": "[74] C. Yang, Y.-M. Cheung, J. Ding, and K. C. Tan, “Concept drift-tolerant transfer learning in dynamic environments,” IEEE Trans. Neural Netw. Learn. Syst., vol. 33, no. 8, pp. 3857–3871, Aug. 2022.",
"translation": "[74] C. Yang, Y.-M. Cheung, J. Ding, and K. C. Tan, “Concept drift-tolerant transfer learning in dynamic environments,” IEEE Trans. Neural Netw. Learn. Syst., vol. 33, no. 8, pp. 3857–3871, Aug. 2022.",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-75",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-75"
],
"translation_ids": [
"zh-reference-75"
],
"source": "[75] The Leader in Decision Intelligence Technology. Accessed: 2024. [Online]. Available: https://www.gurobi.com/",
"translation": "[75] The Leader in Decision Intelligence Technology. Accessed: 2024. [Online]. Available: https://www.gurobi.com/",
"notes": {
"kind": null,
"origin": "source"
}
},
{
"id": "reference-76",
"type": "paragraph",
"section": "参考文献 REFERENCES",
"source_page": null,
"source_ids": [
"reference-76"
],
"translation_ids": [
"zh-reference-76"
],
"source": "[76] A. Koppel, F. Y. Jakubiec, and A. Ribeiro, “A saddle point algorithm for networked online convex optimization,” IEEE Trans. Signal Process., vol. 63, no. 19, pp. 5149–5164, Oct. 2015. Yining Zhang received the B.S. degree in electronic information science and technology from Shanxi University, China, in 2020. She is currently pursuing the Ph.D. degree with the School of Artificial Intelligence, Beijing University of Posts and Telecommunications. Her research interests include online learning, online optimization, and edge AI. Lei Jiao (Member, IEEE) received the Ph.D. degree in computer science from the University of Göttingen, Germany. He is currently with the University of Oregon, USA, and was previously a Member of Technical Staff with Nokia Bell Labs, Ireland. He has published more than 70 papers mainly in leading journals, such as IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, IEEE/ACM TRANSACTIONS ON NETWORKING, IEEE TRANSACTIONS ON MOBILE COMPUTING, and IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, and conferences, such as INFOCOM, MOBIHOC, ICDCS, SECON, and ICNP. His research interests include AI infrastructures, cloud/edge networks, energy systems, cybersecurity, and multimedia. He is a U.S. National Science Foundation CAREER awardee and was a recipient of the Ripple Faculty Fellowship, the Alcatel-Lucent Bell Labs U.K., and Ireland Recognition Award, and the best paper awards of IEEE CNS 2019 and IEEE LANMAN 2013. He has been on the program committees as the Track Chair of ICDCS and as a member of many conferences, such as INFOCOM, MOBIHOC, ICDCS, WWW, and IWQoS, and also served as the Program Chair for multiple workshops with INFOCOM and ICDCS. Konglin Zhu received the master’s degree in computer science from the University of California, Los Angeles, CA, USA, and the Ph.D. degree from the University of Göttingen, Germany, in 2009 and 2014, respectively. He is currently an Associate Professor with Beijing University of Posts and Telecommunications, Beijing, China. His research interests include the Internet of Vehicles, edge computing, and distributed learning. Xiaojun Lin (Fellow, IEEE) received the B.S. degree from Zhongshan University, Guangzhou, China, in 1994, and the M.S. and Ph.D. degrees from Purdue University, West Lafayette, IN, USA, in 2000 and 2005, respectively. He joined the School of Electrical and Computer Engineering, Purdue University, in 2005, and became a Professor of ECE, in 2017. Since June 2023, he has been with the Department of Information Engineering, The Chinese University of Hong Kong, as a Professor and a Global STEM Scholar. His research interests include the analysis, control, and optimization of large and complex networked systems, including both communication networks and power grids. He received the NSF CAREER Award in 2007. He received the 2005 Best Paper of the Year Award from the Journal of Communications and Networks, the IEEE INFOCOM 2008 Best Paper Award, the ACM MobiHoc 2021 Best Paper Award, and the ACM e-Energy 2022 Best Paper Award. He was the Workshop Co-Chair of IEEE GLOBECOM 2007, the Panel Co-Chair of WICON 2008, the TPC Co-Chair of ACM MobiHoc 2009, the Mini-Conference Co-Chair of IEEE INFOCOM 2012, and the General Co-Chair of ACM e-Energy 2019. He served as an Area Editor for Computer Networks (Elsevier), an Associate Editor for IEEE/ACM TRANSACTIONS ON NETWORKING, and the Guest Editor for Ad Hoc Networks (Elsevier). Lin Zhang (Member, IEEE) received the B.S. and Ph.D. degrees from Beijing University of Posts and Telecommunications, Beijing, China, in 1996 and 2001, respectively. From 2000 to 2004, he was a Post-Doctoral Researcher with the Information and Communications University, Daejeon, South Korea, and Nanyang Technological University, Singapore. He joined Beijing University of Posts and Telecommunications in 2004, where he has been a Professor, since 2011. He is currently the Director of Beijing Big Data Center. His current research interests include mobile cloud computing and the Internet of Things. Authorized licensed use limited to: Northeastern University. Downloaded on May 21,2026 at 01:42:46 UTC from IEEE Xplore. Restrictions apply.",
"translation": "[76] A. Koppel, F. Y. Jakubiec, and A. Ribeiro, “A saddle point algorithm for networked online convex optimization,” IEEE Trans. Signal Process., vol. 63, no. 19, pp. 5149–5164, Oct. 2015. Yining Zhang received the B.S. degree in electronic information science and technology from Shanxi University, China, in 2020. She is currently pursuing the Ph.D. degree with the School of Artificial Intelligence, Beijing University of Posts and Telecommunications. Her research interests include online learning, online optimization, and edge AI. Lei Jiao (Member, IEEE) received the Ph.D. degree in computer science from the University of Göttingen, Germany. He is currently with the University of Oregon, USA, and was previously a Member of Technical Staff with Nokia Bell Labs, Ireland. He has published more than 70 papers mainly in leading journals, such as IEEE JOURNAL ON SELECTED AREAS IN COMMUNICATIONS, IEEE/ACM TRANSACTIONS ON NETWORKING, IEEE TRANSACTIONS ON MOBILE COMPUTING, and IEEE TRANSACTIONS ON PARALLEL AND DISTRIBUTED SYSTEMS, and conferences, such as INFOCOM, MOBIHOC, ICDCS, SECON, and ICNP. His research interests include AI infrastructures, cloud/edge networks, energy systems, cybersecurity, and multimedia. He is a U.S. National Science Foundation CAREER awardee and was a recipient of the Ripple Faculty Fellowship, the Alcatel-Lucent Bell Labs U.K., and Ireland Recognition Award, and the best paper awards of IEEE CNS 2019 and IEEE LANMAN 2013. He has been on the program committees as the Track Chair of ICDCS and as a member of many conferences, such as INFOCOM, MOBIHOC, ICDCS, WWW, and IWQoS, and also served as the Program Chair for multiple workshops with INFOCOM and ICDCS. Konglin Zhu received the master’s degree in computer science from the University of California, Los Angeles, CA, USA, and the Ph.D. degree from the University of Göttingen, Germany, in 2009 and 2014, respectively. He is currently an Associate Professor with Beijing University of Posts and Telecommunications, Beijing, China. His research interests include the Internet of Vehicles, edge computing, and distributed learning. Xiaojun Lin (Fellow, IEEE) received the B.S. degree from Zhongshan University, Guangzhou, China, in 1994, and the M.S. and Ph.D. degrees from Purdue University, West Lafayette, IN, USA, in 2000 and 2005, respectively. He joined the School of Electrical and Computer Engineering, Purdue University, in 2005, and became a Professor of ECE, in 2017. Since June 2023, he has been with the Department of Information Engineering, The Chinese University of Hong Kong, as a Professor and a Global STEM Scholar. His research interests include the analysis, control, and optimization of large and complex networked systems, including both communication networks and power grids. He received the NSF CAREER Award in 2007. He received the 2005 Best Paper of the Year Award from the Journal of Communications and Networks, the IEEE INFOCOM 2008 Best Paper Award, the ACM MobiHoc 2021 Best Paper Award, and the ACM e-Energy 2022 Best Paper Award. He was the Workshop Co-Chair of IEEE GLOBECOM 2007, the Panel Co-Chair of WICON 2008, the TPC Co-Chair of ACM MobiHoc 2009, the Mini-Conference Co-Chair of IEEE INFOCOM 2012, and the General Co-Chair of ACM e-Energy 2019. He served as an Area Editor for Computer Networks (Elsevier), an Associate Editor for IEEE/ACM TRANSACTIONS ON NETWORKING, and the Guest Editor for Ad Hoc Networks (Elsevier). Lin Zhang (Member, IEEE) received the B.S. and Ph.D. degrees from Beijing University of Posts and Telecommunications, Beijing, China, in 1996 and 2001, respectively. From 2000 to 2004, he was a Post-Doctoral Researcher with the Information and Communications University, Daejeon, South Korea, and Nanyang Technological University, Singapore. He joined Beijing University of Posts and Telecommunications in 2004, where he has been a Professor, since 2011. He is currently the Director of Beijing Big Data Center. His current research interests include mobile cloud computing and the Internet of Things. Authorized licensed use limited to: Northeastern University. Downloaded on May 21,2026 at 01:42:46 UTC from IEEE Xplore. Restrictions apply.",
"notes": {
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{
"id": "teaching-001",
"type": "paragraph",
"section": "译者教学补充",
"source_page": 4,
"source_ids": [
"teaching-001"
],
"translation_ids": [
"zh-teaching-001"
],
"source": "",
"translation": "**译者教学补充 · 五个算法怎么真的跑起来。** 本节不属于论文正文，是译者为了把五段伪代码讲通而补写的材料，含可手算的小例子。凡涉及具体数字处，都是译者为了说明机制而自设的算例，不是作者的实验数据，不能当作论文结论引用。",
"notes": {
"kind": "blue",
"origin": "source"
}
},
{
"id": "teaching-002",
"type": "paragraph",
"section": "译者教学补充",
"source_page": 4,
"source_ids": [
"teaching-002"
],
"translation_ids": [
"zh-teaching-002"
],
"source": "",
"translation": "**① 一个时隙内到底发生了什么（时间线）。** 原文第 4 页的 “Our Mechanism” 框给出主循环，展开成时间线是：
**(1) 判断是否切换托管集合** —— 算法 4 比较“继续托管的累计成本”与“切换成本的 $k$ 倍”；
**(2) 若切换，解 $\\mathcal{P}^t_3$** 得到新的 $\\bar{y}^t,\\bar{z}^t$；
**(3) 选标** —— 算法 1 在分数域解出 $\\tilde{x}^t$，算法 2 随机舍入成 $\\bar{x}^t\\in\\{0,1\\}$；
**(4) 集成推理** —— 算法 5 对每个样本 $m$ 先算 $\\alpha^t_{n,m},\\beta^t_m$，再得 $\\hat{b}^t_m$ 并返回给用户；
**(5) 收标签并更新权重** —— 用户在样本到达之后才给出 $b^t_m$，算法 5 用它做指数更新；
**(6) 结算** —— 算法 3 对 $\\bar{x}^t_n=1$ 的投标计算支付 $p^t_n$。
关键观察：第 (3) 步与第 (6) 步必须按此顺序——定价要用到算法 1、2 算出的实际分配，所以支付放在最后。",
"notes": {
"kind": "blue",
"origin": "source"
}
},
{
"id": "teaching-003",
"type": "paragraph",
"section": "译者教学补充",
"source_page": 5,
"source_ids": [
"teaching-003"
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"translation_ids": [
"zh-teaching-003"
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"source": "",
"translation": "**② 算法 1 手算例：对偶变量是“慢慢攒”出来的。** 设 $N=2$，两个投标的竞价 $c_1=3$、$c_2=5$；已给定 $y^1=(1,0)$（只有投标 1 必须托管）；预算 $Q^1=2$；参与阈值 $\\phi=(0.5,0.9)$（投标 2 要求更高的参与率）；步长 $\\eta=0.1$，$\\gamma=1$，初值 $\\lambda^1=(0,0)$，上一次的分数解 $\\tilde{x}^1=(1,0)$。
**第一次迭代（第 1 轮）**：
· 对偶上升 (5)：$\\lambda_1^{2}=[0+0.1(0.5-1)]^+=0$，$\\lambda_2^{2}=[0+0.1(0.9-0)]^+=0.09$。
· 下降步 (6)：目标为 $3(x_1-1)+5x_2+0.09(0.9-x_2)+\\frac12[(x_1-1)^2+x_2^2]$。对 $x_1$ 求导得 $3+(x_1-1)=0\\Rightarrow x_1=-2$，受约束 $x_1\\ge y_1=1$ 与 $x_1\\le1$ 夹到 $x_1=1$；对 $x_2$ 求导得 $5-0.09+x_2=0\\Rightarrow x_2=-4.91$，夹到 $x_2=0$。
· 结果 $\\tilde{x}^2=(1,0)$——**投标 2 仍然买不到**。
**要几轮才买得到？** $\\lambda_2$ 每轮增加约 $0.1\\times0.9=0.09$；要让 $x_2>0$，需 $5-\\lambda_2<0$，即 $\\lambda_2>5$，约需 $5/0.09\\approx56$ 轮。
**这说明什么**：长期参与约束 (2c) 不是靠某一步强制满足的，而是靠对偶变量在几十轮里逐渐累积、最终把“贵但需要照顾”的投标推入选择集。这也解释了为什么定理 1 的拟合是 $O(T^{2/3})$——它随时间衰减，但不会在少数几轮内归零。",
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{
"id": "teaching-004",
"type": "paragraph",
"section": "译者教学补充",
"source_page": 5,
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"translation": "**③ 算法 2 手算例：先缩放、再舍入，期望一分不差。** 设分数解 $\\tilde{x}=(0.7,\\,0.4,\\,0.6)$。
**缩放**：$\\epsilon=0.7+0.4+0.6=1.7$，$\\lceil\\epsilon\\rceil=2$，$\\lfloor\\epsilon\\rfloor=1$，故 $\\omega_1=2/1.7=1.176$，$\\omega_2=1/1.7=0.588$。
· 以概率 $\\epsilon-\\lfloor\\epsilon\\rfloor=0.7$ 取 $\\omega_1\\tilde{x}=(0.824,\\,0.471,\\,0.706)$，和为 $2.0$；
· 以概率 $\\lceil\\epsilon\\rceil-\\epsilon=0.3$ 取 $\\omega_2\\tilde{x}=(0.412,\\,0.235,\\,0.353)$，和为 $1.0$。
· 期望：$0.7\\times0.824+0.3\\times0.412=0.700$ ✓（另两个同理）——和为整数，且期望不变。
**舍入**（以第一支为例，取 $n_1=1,n_2=2$）：$\\phi_1=\\min\\{1-0.824,\\,0.471\\}=0.176$，$\\phi_2=\\min\\{1-0.471,\\,0.824\\}=0.529$。
· 概率 $\\phi_2/(\\phi_1+\\phi_2)=0.75$：$(0.824+0.176,\\,0.471-0.176)=(1.0,\\,0.295)$ → $\\bar{x}_1=1$，把 1 号移出 $N'$；
· 概率 $\\phi_1/(\\phi_1+\\phi_2)=0.25$：$(0.824-0.529,\\,0.471+0.529)=(0.295,\\,1.0)$ → $\\bar{x}_2=1$，把 2 号移出 $N'$。
· 校验期望：$0.75\\times1.0+0.25\\times0.295=0.824$ ✓——舍入也没有改变期望。
**为什么两个概率是 $\\phi_2/(\\phi_1+\\phi_2)$ 与 $\\phi_1/(\\phi_1+\\phi_2)$**：设第一支概率为 $p$，要求 $p\\phi_1=(1-p)\\phi_2$（否则期望会漂移），解得 $p=\\phi_2/(\\phi_1+\\phi_2)$。原文该处因双栏排版而分子分母错位，我按此推导填写。",
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{
"id": "teaching-005",
"type": "paragraph",
"section": "译者教学补充",
"source_page": 6,
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"translation": "**④ 算法 3 手算例：付多少钱，以及为什么投标人不亏。** 设中标的投标 $n$ 报告成本 $c_n=0.4$，算法 1 给出的分数分配 $\\tilde{x}_n=0.6$，$\\gamma=1$，$\\lambda_n=0.05$。
**第一步，定积分上限**：$\\chi_n=\\tilde{x}_n/\\gamma+2\\lambda_n=0.6+0.10=0.70$。
**第二步，设定“若竞价变化，分配会怎么变”**：由 $\\chi_n$ 的含义（当 $c\\ge\\chi_n$ 时 $\\tilde{x}_n=0$），取最简单的线性形式 $\\tilde{x}_n(c)=2(0.7-c)$，在 $c=0.4$ 处正好等于 $0.6$ ✓，在 $c=0.7$ 处为 $0$ ✓。
**第三步，算积分**：$\\int_{0.4}^{0.7}2(0.7-c)\\,dc=2\\left[0.7c-\\frac{c^2}{2}\\right]_{0.4}^{0.7}=2\\left[(0.49-0.245)-(0.28-0.08)\\right]=0.09$。
**第四步，得支付**：$p_n=c_n\\tilde{x}_n+0.09=0.4\\times0.6+0.09=0.33$。
**第五步，验证个体理性**：效用 $=p_n-c_n\\tilde{x}_n=0.33-0.24=0.09\\ge0$ ✓。注意支付恰好等于“成本乘以分配”再加一块信息租金 $0.09$——这块租金正是让投标人愿意如实报价（真实性）的原因：报高价会被积分的上限 $\\chi_n$ 截断而失去机会，报低价则拿到更少的租金。",
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{
"id": "teaching-006",
"type": "paragraph",
"section": "译者教学补充",
"source_page": 7,
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"translation": "**⑤ 算法 4 手算例：什么时候才值得“切换一次”。** 设切换常数 $k=2$。
· $t=1$：$\\hat{t}=1$，解 $\\mathcal{P}^1_3$ 得 $\\bar{y}^1$，本轮切换成本 $C^1_{SC}=1.0$，本轮非切换成本 $C^1_{-SC}=1.5$。
· $t=2$：若改用新集合，切换成本 $C^2_{SC}=1.0$，自 $\\hat{t}=1$ 以来累计非切换成本 $=C^1_{-SC}=1.5$。判据 $k\\,C^2_{SC}\\le\\sum_{\\tau=\\hat t}^{t-1}C^\\tau_{-SC}$ 即 $2\\times1.0=2.0\\le1.5$？不成立 → 不切换，保持 $\\bar{y}^2=\\bar{y}^1$。
· $t=3$：累计非切换成本 $=1.5+1.4=2.9$。判据 $2.0\\le2.9$ 成立 → 切换，解 $\\mathcal{P}^3_3$ 得新集合，$\\hat{t}=3$。
**这说明什么**：$k$ 是一根“耐心旋钮”——$k$ 越大，就越要等累计成本攒得更多才肯切换，于是切换更少、切换成本总量更小；而每次切换后计时器 $\\hat{t}$ 归零，重新开始攒。原文由此得到 $\\sum_t C^t_{SC}\\le\\frac1k\\sum_t C^t_{-SC}$，把难管的切换成本折算成非切换成本的 $1/k$。",
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{
"id": "teaching-007",
"type": "paragraph",
"section": "译者教学补充",
"source_page": 7,
"source_ids": [
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"translation": "**⑥ 算法 5 手算例：指数更新有多“狠”。** 设只有 1 个外购模型加自有模型，二者都已托管，故 $\\xi_{1,1}=\\bar{y}_1=1$、$\\psi_1=\\bar{z}=1$。
**样本 $m=1$**：$\\alpha=\\frac{1}{1+1}=0.5$，$\\beta=0.5$。设外购模型预测正确 $h_1(a)=1$、自有模型预测错误 $h(a)=0$，真实标签 $b=1$，平方损失 $l(h,b)=(h-b)^2$，于是 $l_1=0$、$l_{\\text{own}}=1$。
联合结果 $\\hat{b}=0.5\\times1+0.5\\times0=0.5$。
**步长**：$\\mu_1=\\sqrt{8\\ln I_1/1}=\\sqrt{8\\ln2}=\\sqrt{5.545}=2.354$。
**更新**：$\\xi_{1,2}=1\\cdot e^{-2.354\\times0}=1$；$\\psi_2=1\\cdot e^{-2.354\\times1}=0.0948$。
**样本 $m=2$**：$\\alpha=\\frac{1}{1+0.0948}=0.9134$，$\\beta=0.0866$。
**读数**：只一个样本之后，好模型的权重就从 $0.50$ 升到 $0.9134$，差模型从 $0.50$ 掉到 $0.0866$——这就是指数（乘性）更新的威力：表现差的模型权重按 $e^{-\\mu\\cdot\\text{loss}}$ 连乘而迅速衰减，无需显式淘汰规则。第 10 行“接收真实标签”夹在推理与更新之间，恰好体现了“先推理、后见标签”的在线顺序。",
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{
"id": "teaching-008",
"type": "paragraph",
"section": "译者教学补充",
"source_page": 8,
"source_ids": [
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"translation_ids": [
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"translation": "**⑦ 五算法复杂度与“谁管什么”的对照。**\n\n| 算法 | 管什么 | 关键机制 | 复杂度 |\n|---|---|---|---|\n| 1 在线分数 | 本轮买哪些投标（分数域） | 原始–对偶交替：$\\lambda$ 上升、$x$ 下降 | 内点法 $O(N^2\\log(1/\\nu))$ |\n| 2 随机舍入 | 把分数变成 0/1 | 先缩放使和为整数，再相依舍入，期望不变 | $O(N)$ |\n| 3 支付分配 | 付给中标者多少钱 | 临界支付 + 积分信息租金 | $O(N^3 i\\log(1/\\nu))$ |\n| 4 模型托管 | 哪些模型留在本地 | 懒惰切换：$k\\,C_{SC}\\le\\sum C_{-SC}$ 才切换 | $O(T\\cdot N^2\\log(1/\\nu))$ |\n| 5 集成学习 | 各模型投票权重 | Hedge 指数更新 | $O(NM^t)$ |\n\n**读表要点**：算法 3 是全文最贵的一步（$N^3$ 且含数值积分分段数 $i$），原文实验里也承认它“对时延不敏感、可在一分钟内算完”——这正是它被放在每时隙最后、且允许慢的原因。",
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{
"id": "teaching-009",
"type": "paragraph",
"section": "译者教学补充",
"source_page": 8,
"source_ids": [
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"translation_ids": [
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"translation": "**⑧ 读这篇论文最容易弄错的六处。**
**(1) 把 $\\tilde{x}$ 与 $\\bar{x}$ 混用**：$\\tilde{x}$ 是算法 1 的分数解（可为 0.7），$\\bar{x}$ 是算法 2 的整数输出（只能是 0 或 1）。定理 2 的条件是对 $\\mathbb{E}(\\bar{x})$ 说的，而算法 1 只给 $\\tilde{x}$，所以必须靠算法 2 的“期望保持”把两者接起来。
**(2) 以为 $C^t_{SC}$（切换成本）和 $C^t_{-SC}$（非切换成本）是一对反义词**：$C^t_{-SC}$ 的“$-SC$”表示“不含切换成本”，它包含购买成本 $\\sum x^tc^t$、托管成本与自有模型成本；两者相加才是总社会成本。
**(3) 把定理 1 的 $O(T^{2/3})$ 当成“每步误差”**：它是累计量，摊到每步是 $O(T^{-1/3})\\to0$。
**(4) 以为长期参与约束在每轮都被满足**：它在算法 1 中被吸收进目标，只被渐近满足，其违反量由“动态拟合”量化。
**(5) 把 $Q^t$ 当金额**：$Q^t$ 是“最多可购买的模型个数”，不是预算金额（原文措辞是 the maximum number of models）。
**(6) 把定理 4 的 $C^*$ 当成 $\\mathcal{P}_0$ 的离线最优**：$C^*$ 用的是“离线最优的社会成本（不含损失）＋逐时隙单个最佳模型的损失累加”，是一个混合基准；原文明确说明这不是直接与离线最优比较，理由是要与“从专家中学习”的惯例对齐。",
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{
"id": "teaching-010",
"type": "paragraph",
"section": "译者教学补充",
"source_page": 8,
"source_ids": [
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"translation": "**⑨ 一句话串起全文的因果链。**
概念漂移 ⇒ 单模型精度下降 ⇒ 用集成（算法 5）补精度 ⇒ 集成需要更多模型 ⇒ 模型要向提供方买 ⇒ 用重复拍卖（算法 1、2、3）压低购买成本并保证真实性 ⇒ 买来的模型要留在本地才划算 ⇒ 用懒惰切换（算法 4）平衡切换与托管成本 ⇒ 但“留哪些模型”又反过来影响拍卖的估值 ⇒ 于是整条链必须联合优化，这正是问题 $\\mathcal{P}_0$ 与“后端（拍卖+托管）＋前端（集成）”两段式设计的由来。",
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]