Mathematics of Operations Research最新文献_第9页

Towards Optimal Problem Dependent Generalization Error Bounds in Statistical Learning Theory 在统计学习理论中实现与问题相关的最优泛化误差界限

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-01-19 DOI: 10.1287/moor.2021.0076

Yunbei Xu, Assaf Zeevi

{"title":"Towards Optimal Problem Dependent Generalization Error Bounds in Statistical Learning Theory","authors":"Yunbei Xu, Assaf Zeevi","doi":"10.1287/moor.2021.0076","DOIUrl":"https://doi.org/10.1287/moor.2021.0076","url":null,"abstract":"We study problem-dependent rates, that is, generalization errors that scale near-optimally with the variance, effective loss, or gradient norms evaluated at the “best hypothesis.” We introduce a principled framework dubbed “uniform localized convergence” and characterize sharp problem-dependent rates for central statistical learning problems. From a methodological viewpoint, our framework resolves several fundamental limitations of existing uniform convergence and localization analysis approaches. It also provides improvements and some level of unification in the study of localized complexities, one-sided uniform inequalities, and sample-based iterative algorithms. In the so-called “slow rate” regime, we provide the first (moment-penalized) estimator that achieves the optimal variance-dependent rate for general “rich” classes; we also establish an improved loss-dependent rate for standard empirical risk minimization. In the “fast rate” regime, we establish finite-sample, problem-dependent bounds that are comparable to precise asymptotics. In addition, we show that iterative algorithms such as gradient descent and first order expectation maximization can achieve optimal generalization error in several representative problems across the areas of nonconvex learning, stochastic optimization, and learning with missing data.Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2021.0076 .","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139517379","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Online Saddle Point Problem and Online Convex Optimization with Knapsacks 带包的在线鞍点问题和在线凸优化

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-01-12 DOI: 10.1287/moor.2018.0330

Adrian Rivera Cardoso, He Wang, Huan Xu

{"title":"The Online Saddle Point Problem and Online Convex Optimization with Knapsacks","authors":"Adrian Rivera Cardoso, He Wang, Huan Xu","doi":"10.1287/moor.2018.0330","DOIUrl":"https://doi.org/10.1287/moor.2018.0330","url":null,"abstract":"We study the online saddle point problem, an online learning problem where at each iteration, a pair of actions needs to be chosen without knowledge of the current and future (convex-concave) payoff functions. The objective is to minimize the gap between the cumulative payoffs and the saddle point value of the aggregate payoff function, which we measure using a metric called saddle point regret (SP-Regret). The problem generalizes the online convex optimization framework, but here, we must ensure that both players incur cumulative payoffs close to that of the Nash equilibrium of the sum of the games. We propose an algorithm that achieves SP-Regret proportional to [Formula: see text] in the general case, and [Formula: see text] SP-Regret for the strongly convex-concave case. We also consider the special case where the payoff functions are bilinear and the decision sets are the probability simplex. In this setting, we are able to design algorithms that reduce the bounds on SP-Regret from a linear dependence in the dimension of the problem to a logarithmic one. We also study the problem under bandit feedback and provide an algorithm that achieves sublinear SP-Regret. We then consider an online convex optimization with knapsacks problem motivated by a wide variety of applications, such as dynamic pricing, auctions, and crowdsourcing. We relate this problem to the online saddle point problem and establish [Formula: see text] regret using a primal-dual algorithm.","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139460720","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Strategy-Proof Multidimensional Mechanism Design 策略可靠的多维机制设计

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-01-10 DOI: 10.1287/moor.2022.0324

Ranojoy Basu, Conan Mukherjee

引用次数: 0

The Privacy Paradox and Optimal Bias–Variance Trade-offs in Data Acquisition 数据采集中的隐私悖论与偏差-方差的最佳权衡

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-01-09 DOI: 10.1287/moor.2023.0022

Guocheng Liao, Yu Su, Juba Ziani, Adam Wierman, Jianwei Huang

{"title":"The Privacy Paradox and Optimal Bias–Variance Trade-offs in Data Acquisition","authors":"Guocheng Liao, Yu Su, Juba Ziani, Adam Wierman, Jianwei Huang","doi":"10.1287/moor.2023.0022","DOIUrl":"https://doi.org/10.1287/moor.2023.0022","url":null,"abstract":"Whereas users claim to be concerned about privacy, often they do little to protect their privacy in their online actions. One prominent explanation for this privacy paradox is that, when an individual shares data, it is not just the individual’s privacy that is compromised; the privacy of other individuals with correlated data is also compromised. This information leakage encourages oversharing of data and significantly impacts the incentives of individuals in online platforms. In this paper, we study the design of mechanisms for data acquisition in settings with information leakage and verifiable data. We design an incentive-compatible mechanism that optimizes the worst case trade-off between bias and variance of the estimation subject to a budget constraint, with which the worst case is over the unknown correlation between costs and data. Additionally, we characterize the structure of the optimal mechanism in closed form and study monotonicity and nonmonotonicity properties of the marketplace.Funding: This work is supported by the National Natural Science Foundation of China [Grants 62202512 and 62271434], Shenzhen Science and Technology Program [Grant JCYJ20210324120011032], Guangdong Basic and Applied Basic Research Foundation [Grant 2021B1515120008], Shenzhen Key Laboratory of Crowd Intelligence Empowered Low-Carbon Energy Network [Grant ZDSYS20220606100601002], and the Shenzhen Institute of Artificial Intelligence and Robotics for Society. This work is also supported by the National Science Foundation [Grants CNS-2146814, CPS-2136197, CNS-2106403, and NGSDI-2105648].Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2023.0022 .","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-01-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139410295","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

The Multi-Objective Polynomial Optimization 多目标多项式优化

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-01-04 DOI: 10.1287/moor.2023.0200

Jiawang Nie, Zi Yang

引用次数: 0

Diffusion-Based Staffing for Multitasking Service Systems with Many Servers 多服务器多任务服务系统的基于扩散的人员配置

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2023-12-28 DOI: 10.1287/moor.2021.0051

Jaap Storm, Wouter Berkelmans, René Bekker

{"title":"Diffusion-Based Staffing for Multitasking Service Systems with Many Servers","authors":"Jaap Storm, Wouter Berkelmans, René Bekker","doi":"10.1287/moor.2021.0051","DOIUrl":"https://doi.org/10.1287/moor.2021.0051","url":null,"abstract":"We consider a many-server queue in which each server can serve multiple customers in parallel. Such multitasking phenomena occur in various applications areas (e.g., in hospitals and contact centers), although the impact of the number of customers who are simultaneously served on system efficiency may vary. We establish diffusion limits of the queueing process under the quality-and-efficiency-driven scaling and for different policies of assigning customers to servers depending on the number of customers they serve. We show that for a broad class of routing policies, including routing to the least busy server, the same one-dimensional diffusion process is obtained in the heavy-traffic limit. In case of assignment to the most busy server, there is no state-space collapse, and the diffusion limit involves a custom regulator mapping. Moreover, we also show that assigning customers to the least (most) busy server is optimal when the cumulative service rate per server is concave (convex), motivating the routing policies considered. Finally, we also derive diffusion limits in the nonheavy-traffic scaling regime and in the heavy-traffic scaling regime where customers can be reassigned during service.Funding: The research of J. Storm is partly funded by the Netherlands Organization for Scientific Research (NWO) Gravitation project Networks [Grant 024.002.003].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139067240","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Learning-Augmented Mechanism Design: Leveraging Predictions for Facility Location 学习增强机制设计：利用预测确定设施位置

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2023-12-27 DOI: 10.1287/moor.2022.0225

Priyank Agrawal, Eric Balkanski, Vasilis Gkatzelis, Tingting Ou, Xizhi Tan

{"title":"Learning-Augmented Mechanism Design: Leveraging Predictions for Facility Location","authors":"Priyank Agrawal, Eric Balkanski, Vasilis Gkatzelis, Tingting Ou, Xizhi Tan","doi":"10.1287/moor.2022.0225","DOIUrl":"https://doi.org/10.1287/moor.2022.0225","url":null,"abstract":"In this work, we introduce an alternative model for the design and analysis of strategyproof mechanisms that is motivated by the recent surge of work in “learning-augmented algorithms.” Aiming to complement the traditional worst-case analysis approach in computer science, this line of work has focused on the design and analysis of algorithms that are enhanced with machine-learned predictions. The algorithms can use the predictions as a guide to inform their decisions, aiming to achieve much stronger performance guarantees when these predictions are accurate (consistency), while also maintaining near-optimal worst-case guarantees, even if these predictions are inaccurate (robustness). We initiate the design and analysis of strategyproof mechanisms that are augmented with predictions regarding the private information of the participating agents. To exhibit the important benefits of this approach, we revisit the canonical problem of facility location with strategic agents in the two-dimensional Euclidean space. We study both the egalitarian and utilitarian social cost functions, and we propose new strategyproof mechanisms that leverage predictions to guarantee an optimal trade-off between consistency and robustness. Furthermore, we also prove parameterized approximation results as a function of the prediction error, showing that our mechanisms perform well, even when the predictions are not fully accurate.Funding: The work of E. Balkanski was supported in part by the National Science Foundation [Grants CCF-2210501 and IIS-2147361]. The work of V. Gkatzelis and X. Tan was supported in part by the National Science Foundation [Grant CCF-2210502] and [CAREER Award CCF-2047907].Supplemental Material: The e-companion is available at https://doi.org/10.1287/moor.2022.0225 .","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139053488","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Limit Theorems for Default Contagion and Systemic Risk 违约传染和系统风险的极限定理

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2023-12-27 DOI: 10.1287/moor.2021.0283

Hamed Amini, Zhongyuan Cao, Agnès Sulem

引用次数: 0

Zero-One Composite Optimization: Lyapunov Exact Penalty and a Globally Convergent Inexact Augmented Lagrangian Method 零一复合优化：李雅普诺夫精确惩罚和全球收敛的不精确增量拉格朗日方法

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2023-12-22 DOI: 10.1287/moor.2021.0320

Penghe Zhang, Naihua Xiu, Ziyan Luo

{"title":"Zero-One Composite Optimization: Lyapunov Exact Penalty and a Globally Convergent Inexact Augmented Lagrangian Method","authors":"Penghe Zhang, Naihua Xiu, Ziyan Luo","doi":"10.1287/moor.2021.0320","DOIUrl":"https://doi.org/10.1287/moor.2021.0320","url":null,"abstract":"We consider the problem of minimizing the sum of a smooth function and a composition of a zero-one loss function with a linear operator, namely the zero-one composite optimization problem (0/1-COP). It has a vast body of applications, including the support vector machine (SVM), calcium dynamics fitting (CDF), one-bit compressive sensing (1-bCS), and so on. However, it remains challenging to design a globally convergent algorithm for the original model of 0/1-COP because of the nonconvex and discontinuous zero-one loss function. This paper aims to develop an inexact augmented Lagrangian method (IALM), in which the generated whole sequence converges to a local minimizer of 0/1-COP under reasonable assumptions. In the iteration process, IALM performs minimization on a Lyapunov function with an adaptively adjusted multiplier. The involved Lyapunov penalty subproblem is shown to admit the exact penalty theorem for 0/1-COP, provided that the multiplier is optimal in the sense of the proximal-type stationarity. An efficient zero-one Bregman alternating linearized minimization algorithm is also designed to achieve an approximate solution of the underlying subproblem in finite steps. Numerical experiments for handling SVM, CDF, and 1-bCS demonstrate the satisfactory performance of the proposed method in terms of solution accuracy and time efficiency. Funding: This work was supported by the Fundamental Research Funds for the Central Universities [Grant 2022YJS099] and the National Natural Science Foundation of China [Grants 12131004 and 12271022].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138947219","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Counting and Enumerating Optimum Cut Sets for Hypergraph k-Partitioning Problems for Fixed k 计数和枚举固定 k 的超图 k 分区问题的最优切割集

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2023-12-13 DOI: 10.1287/moor.2022.0259

Calvin Beideman, Karthekeyan Chandrasekaran, Weihang Wang

{"title":"Counting and Enumerating Optimum Cut Sets for Hypergraph k-Partitioning Problems for Fixed k","authors":"Calvin Beideman, Karthekeyan Chandrasekaran, Weihang Wang","doi":"10.1287/moor.2022.0259","DOIUrl":"https://doi.org/10.1287/moor.2022.0259","url":null,"abstract":"We consider the problem of enumerating optimal solutions for two hypergraph k-partitioning problems, namely, Hypergraph-k-Cut and Minmax-Hypergraph-k-Partition. The input in hypergraph k-partitioning problems is a hypergraph [Formula: see text] with positive hyperedge costs along with a fixed positive integer k. The goal is to find a partition of V into k nonempty parts [Formula: see text]—known as a k-partition—so as to minimize an objective of interest. (1) If the objective of interest is the maximum cut value of the parts, then the problem is known as Minmax-Hypergraph-k-Partition. A subset of hyperedges is a minmax-k-cut-set if it is the subset of hyperedges crossing an optimum k-partition for Minmax-Hypergraph-k-Partition. (2) If the objective of interest is the total cost of hyperedges crossing the k-partition, then the problem is known as Hypergraph-k-Cut. A subset of hyperedges is a min-k-cut-set if it is the subset of hyperedges crossing an optimum k-partition for Hypergraph-k-Cut. We give the first polynomial bound on the number of minmax-k-cut-sets and a polynomial-time algorithm to enumerate all of them in hypergraphs for every fixed k. Our technique is strong enough to also enable an [Formula: see text]-time deterministic algorithm to enumerate all min-k-cut-sets in hypergraphs, thus improving on the previously known [Formula: see text]-time deterministic algorithm, in which n is the number of vertices and p is the size of the hypergraph. The correctness analysis of our enumeration approach relies on a structural result that is a strong and unifying generalization of known structural results for Hypergraph-k-Cut and Minmax-Hypergraph-k-Partition. We believe that our structural result is likely to be of independent interest in the theory of hypergraphs (and graphs).Funding: All authors were supported by NSF AF 1814613 and 1907937.","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2023-12-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138630708","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0