Mathematics of Operations Research最新文献_第4页

ρ-Arbitrage and ρ-Consistent Pricing for Star-Shaped Risk Measures 星形风险度量的 ρ 套利和 ρ 一致性定价

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-09 DOI: 10.1287/moor.2023.0173

Martin Herdegen, Nazem Khan

引用次数: 0

Rank-One Boolean Tensor Factorization and the Multilinear Polytope 一阶布尔张量因式分解与多线性多面体

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-09 DOI: 10.1287/moor.2022.0201

Alberto Del Pia, Aida Khajavirad

{"title":"Rank-One Boolean Tensor Factorization and the Multilinear Polytope","authors":"Alberto Del Pia, Aida Khajavirad","doi":"10.1287/moor.2022.0201","DOIUrl":"https://doi.org/10.1287/moor.2022.0201","url":null,"abstract":"We consider the NP-hard problem of finding the closest rank-one binary tensor to a given binary tensor, which we refer to as the rank-one Boolean tensor factorization (BTF) problem. This optimization problem can be used to recover a planted rank-one tensor from noisy observations. We formulate rank-one BTF as the problem of minimizing a linear function over a highly structured multilinear set. Leveraging on our prior results regarding the facial structure of multilinear polytopes, we propose novel linear programming relaxations for rank-one BTF. We then establish deterministic sufficient conditions under which our proposed linear programs recover a planted rank-one tensor. To analyze the effectiveness of these deterministic conditions, we consider a semirandom model for the noisy tensor and obtain high probability recovery guarantees for the linear programs. Our theoretical results as well as numerical simulations indicate that certain facets of the multilinear polytope significantly improve the recovery properties of linear programming relaxations for rank-one BTF.Funding: A. Del Pia is partially funded by the Air Force Office of Scientific Research [Grant FA9550-23-1-0433]. A. Khajavirad is partially funded by the Air Force Office of Scientific Research [Grant FA9550-23-1-0123].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568732","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

Hidden Convexity, Optimization, and Algorithms on Rotation Matrices 旋转矩阵的隐凸性、优化和算法

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-01 DOI: 10.1287/moor.2023.0114

Akshay Ramachandran, Kevin Shu, Alex L. Wang

{"title":"Hidden Convexity, Optimization, and Algorithms on Rotation Matrices","authors":"Akshay Ramachandran, Kevin Shu, Alex L. Wang","doi":"10.1287/moor.2023.0114","DOIUrl":"https://doi.org/10.1287/moor.2023.0114","url":null,"abstract":"This paper studies hidden convexity properties associated with constrained optimization problems over the set of rotation matrices [Formula: see text]. Such problems are nonconvex because of the constraint [Formula: see text]. Nonetheless, we show that certain linear images of [Formula: see text] are convex, opening up the possibility for convex optimization algorithms with provable guarantees for these problems. Our main technical contributions show that any two-dimensional image of [Formula: see text] is convex and that the projection of [Formula: see text] onto its strict upper triangular entries is convex. These results allow us to construct exact convex reformulations for constrained optimization problems over [Formula: see text] with a single constraint or with constraints defined by low-rank matrices. Both of these results are maximal in a formal sense.Funding: A. Ramachandran was supported by the H2020 program of the European Research Council [Grant 805241-QIP]. A. L. Wang was supported by the Nederlandse Organisatie voor Wetenschappelijk Onderzoek [Grant OCENW.GROOT.2019.015 (OPTIMAL)]. K. Shu was supported by the Georgia Institute of Technology (ACO-ARC fellowship).","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141505983","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

Procuring Unverifiable Information 获取不可逆转的信息

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-06-10 DOI: 10.1287/moor.2022.0085

Salil Sharma, E. Tsakas, M. Voorneveld

{"title":"Procuring Unverifiable Information","authors":"Salil Sharma, E. Tsakas, M. Voorneveld","doi":"10.1287/moor.2022.0085","DOIUrl":"https://doi.org/10.1287/moor.2022.0085","url":null,"abstract":"We study settings where information in the form of Bayesian signals is acquired by an expert on behalf of a principal. Information acquisition is costly for the expert and crucially not verifiable by the principal. The expert is compensated by the principal with a menu of state-contingent payments. We provide a full characterization of the set of all menus that implement (respectively, strictly implement) each signal. Moreover, we provide a closed-form characterization for the expected cost for the cheapest such menu, which we call proxy cost of the signal. Surprisingly, in general, the proxy cost is neither increasing in the Blackwell order nor posterior separable, even when the expert’s cost function is posterior separable itself. Subsequently, we study the full-agency problem (by introducing a downstream decision), thus endogenizing the signal. We show that there is always an optimal signal that can be strictly implemented, meaning that it is without loss of generality to exogenously restrict attention to strict implementation. As a result, similarly to Bayesian persuasion, the complexity of the principal’s optimal signal is bounded by the cardinality of the state space. Finally, we present some applications of interest. Funding: Financial support by the Wallander-Hedelius Foundation [Grants P2016-0072:1 and P20-0035 (to S. Sharma and M. Voorneveld)] is gratefully acknowledged.","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-06-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141360629","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

Confidence Intervals for Piecewise Normal Distributions and Stochastic Variational Inequalities 片断正态分布的置信区间和随机变量不等式

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-05-24 DOI: 10.1287/moor.2023.0021

Shu Lu

引用次数: 0

Corruption-Robust Exploration in Episodic Reinforcement Learning 情节强化学习中的腐败-稳健探索

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-05-23 DOI: 10.1287/moor.2021.0202

Thodoris Lykouris, Max Simchowitz, Aleksandrs Slivkins, Wen Sun

{"title":"Corruption-Robust Exploration in Episodic Reinforcement Learning","authors":"Thodoris Lykouris, Max Simchowitz, Aleksandrs Slivkins, Wen Sun","doi":"10.1287/moor.2021.0202","DOIUrl":"https://doi.org/10.1287/moor.2021.0202","url":null,"abstract":"We initiate the study of episodic reinforcement learning (RL) under adversarial corruptions in both the rewards and the transition probabilities of the underlying system, extending recent results for the special case of multiarmed bandits. We provide a framework that modifies the aggressive exploration enjoyed by existing reinforcement learning approaches based on optimism in the face of uncertainty by complementing them with principles from action elimination. Importantly, our framework circumvents the major challenges posed by naively applying action elimination in the RL setting, as formalized by a lower bound we demonstrate. Our framework yields efficient algorithms that (a) attain near-optimal regret in the absence of corruptions and (b) adapt to unknown levels of corruption, enjoying regret guarantees that degrade gracefully in the total corruption encountered. To showcase the generality of our approach, we derive results for both tabular settings (where states and actions are finite) and linear Markov decision process settings (where the dynamics and rewards admit a linear underlying representation). Notably, our work provides the first sublinear regret guarantee that accommodates any deviation from purely independent and identically distributed transitions in the bandit-feedback model for episodic reinforcement learning.Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2021.0202 .","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146375","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

Markov Decision Processes with Observation Costs: Framework and Computation with a Penalty Scheme 带观察成本的马尔可夫决策过程：框架与惩罚方案计算

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-05-23 DOI: 10.1287/moor.2023.0172

Christoph Reisinger, Jonathan Tam

引用次数: 0

Robust Multiple Stopping—A Duality Approach 稳健的多重停止--二元方法

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-05-15 DOI: 10.1287/moor.2021.0237

R. Laeven, John G. M. Schoenmakers, Nikolaus Schweizer, M. Stadje

{"title":"Robust Multiple Stopping—A Duality Approach","authors":"R. Laeven, John G. M. Schoenmakers, Nikolaus Schweizer, M. Stadje","doi":"10.1287/moor.2021.0237","DOIUrl":"https://doi.org/10.1287/moor.2021.0237","url":null,"abstract":"We develop a method to solve, theoretically and numerically, general optimal stopping problems. Our general setting allows for multiple exercise rights—that is, optimal multiple stopping—for a robust evaluation that accounts for model uncertainty with a dominated family of priors and for general reward processes driven by multidimensional jump-diffusions. Our approach relies on first establishing robust martingale dual representation results for the multiple stopping problem that satisfy appealing almost sure pathwise optimality properties. Next, we exploit these theoretical results to develop upper and lower bounds that, as we formally show, not only converge to the true solution asymptotically, but also constitute genuine prelimiting upper and lower bounds. We illustrate the applicability of our approach in a few examples and analyze the impact of model uncertainty on optimal multiple stopping strategies. Funding: R. J. A. Laeven received financial support from the Netherlands Organization for Scientific Research (NWO) [Grants NWO-Vidi and NWO-Vici]. J. G. M. Schoenmakers received financial support from the Deutsche Forschungsgemeinschaft Excellence Cluster Math+ Berlin [Project AA4-2]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/moor.2021.0237 .","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140972511","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: 1

Liquid Welfare Guarantees for No-Regret Learning in Sequential Budgeted Auctions 连续预算拍卖中无悔学习的流动福利保证

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-05-14 DOI: 10.1287/moor.2023.0274

Giannis Fikioris, Éva Tardos

{"title":"Liquid Welfare Guarantees for No-Regret Learning in Sequential Budgeted Auctions","authors":"Giannis Fikioris, Éva Tardos","doi":"10.1287/moor.2023.0274","DOIUrl":"https://doi.org/10.1287/moor.2023.0274","url":null,"abstract":"We study the liquid welfare in sequential first-price auctions with budgeted buyers. We use a behavioral model for the buyers, assuming a learning style guarantee: the utility of each buyer is within a [Formula: see text] factor ([Formula: see text]) of the utility achievable by shading their value with the same factor at each iteration. We show a [Formula: see text] price of anarchy for liquid welfare when valuations are additive. This is in stark contrast to sequential second-price auctions, where the resulting liquid welfare can be arbitrarily smaller than the maximum liquid welfare, even when [Formula: see text]. We prove a lower bound of [Formula: see text] on the liquid welfare loss under the given assumption in first-price auctions. Our liquid welfare results extend when buyers have submodular valuations over the set of items they win across iterations with a slightly worse price of anarchy bound of [Formula: see text] compared with the guarantee for the additive case.Funding: G. Fikioris is supported in part by the Air Force Office of Scientific Research [Grants FA9550-19-1-0183 and FA9550-23-1-0068], the Department of Defense (DoD) through the National Defense Science & Engineering Graduate (NDSEG) Fellowship Program, and the Onassis Foundation [Scholarship ID F ZS 068-1/2022-2023]. É. Tardos is supported in part by the NSF [Grant CCF-1408673] and AFOSR [Grants FA9550-19-1-0183, FA9550-23-1-0410, and FA9550-23-1-0068].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":null,"pages":null},"PeriodicalIF":1.7,"publicationDate":"2024-05-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141146378","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

A Theory of Alternating Paths and Blossoms from the Perspective of Minimum Length 从最小长度的角度看交替路径和花朵理论

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-05-07 DOI: 10.1287/moor.2020.0388

Vijay V. Vazirani

引用次数: 0