Mathematics of Operations Research最新文献_第3页

Risk-Averse Markov Decision Processes Through a Distributional Lens 从分布角度看风险厌恶马尔可夫决策过程

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-17 DOI: 10.1287/moor.2023.0211

Ziteng Cheng, Sebastian Jaimungal

引用次数: 0

On the Convex Formulations of Robust Markov Decision Processes 论鲁棒性马尔可夫决策过程的凸公式

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-16 DOI: 10.1287/moor.2022.0284

Julien Grand-Clément, Marek Petrik

{"title":"On the Convex Formulations of Robust Markov Decision Processes","authors":"Julien Grand-Clément, Marek Petrik","doi":"10.1287/moor.2022.0284","DOIUrl":"https://doi.org/10.1287/moor.2022.0284","url":null,"abstract":"Robust Markov decision processes (MDPs) are used for applications of dynamic optimization in uncertain environments and have been studied extensively. Many of the main properties and algorithms of MDPs, such as value iteration and policy iteration, extend directly to RMDPs. Surprisingly, there is no known analog of the MDP convex optimization formulation for solving RMDPs. This work describes the first convex optimization formulation of RMDPs under the classical sa-rectangularity and s-rectangularity assumptions. By using entropic regularization and exponential change of variables, we derive a convex formulation with a number of variables and constraints polynomial in the number of states and actions, but with large coefficients in the constraints. We further simplify the formulation for RMDPs with polyhedral, ellipsoidal, or entropy-based uncertainty sets, showing that, in these cases, RMDPs can be reformulated as conic programs based on exponential cones, quadratic cones, and nonnegative orthants. Our work opens a new research direction for RMDPs and can serve as a first step toward obtaining a tractable convex formulation of RMDPs.Funding: The work in the paper was supported, in part, by NSF [Grants 2144601 and 1815275]; and Agence Nationale de la Recherche [Grant 11-LABX-0047].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"34 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141721356","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

Optimality Conditions in Control Problems with Random State Constraints in Probabilistic or Almost Sure Form 具有概率或几乎确定形式随机状态约束的控制问题中的最优性条件

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-15 DOI: 10.1287/moor.2023.0177

Caroline Geiersbach, René Henrion

{"title":"Optimality Conditions in Control Problems with Random State Constraints in Probabilistic or Almost Sure Form","authors":"Caroline Geiersbach, René Henrion","doi":"10.1287/moor.2023.0177","DOIUrl":"https://doi.org/10.1287/moor.2023.0177","url":null,"abstract":"In this paper, we discuss optimality conditions for optimization problems involving random state constraints, which are modeled in probabilistic or almost sure form. Although the latter can be understood as the limiting case of the former, the derivation of optimality conditions requires substantially different approaches. We apply them to a linear elliptic partial differential equation with random inputs. In the probabilistic case, we rely on the spherical-radial decomposition of Gaussian random vectors in order to formulate fully explicit optimality conditions involving a spherical integral. In the almost sure case, we derive optimality conditions and compare them with a model based on robust constraints with respect to the (compact) support of the given distribution.Funding: The authors thank the Deutsche Forschungsgemeinschaft [Projects B02 and B04 in the “Sonderforschungsbereich/Transregio 154 Mathematical Modelling, Simulation and Optimization Using the Example of Gas Networks”] for support. C. Geiersbach acknowledges support from the Deutsche Forschungsgemeinschaft [Germany’s Excellence Strategy–the Berlin Mathematics Research Center MATH+ Grant EXC-2046/1, Project 390685689]. R. Henrion acknowledges support from the Fondation Mathématique Jacques Hadamard [Program Gaspard Monge in Optimization and Operations Research, including support to this program by Electricité de France].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"308 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141721355","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

Large Independent Sets in Recursive Markov Random Graphs 递归马尔可夫随机图中的大独立集

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-12 DOI: 10.1287/moor.2022.0215

Akshay Gupte, Yiran Zhu

{"title":"Large Independent Sets in Recursive Markov Random Graphs","authors":"Akshay Gupte, Yiran Zhu","doi":"10.1287/moor.2022.0215","DOIUrl":"https://doi.org/10.1287/moor.2022.0215","url":null,"abstract":"Computing the maximum size of an independent set in a graph is a famously hard combinatorial problem that has been well studied for various classes of graphs. When it comes to random graphs, the classic Erdős–Rényi–Gilbert random graph [Formula: see text] has been analyzed and shown to have the largest independent sets of size [Formula: see text] with high probability (w.h.p.) This classic model does not capture any dependency structure between edges that can appear in real-world networks. We define random graphs [Formula: see text] whose existence of edges is determined by a Markov process that is also governed by a decay parameter [Formula: see text]. We prove that w.h.p. [Formula: see text] has independent sets of size [Formula: see text] for arbitrary [Formula: see text]. This is derived using bounds on the terms of a harmonic series, a Turán bound on a stability number, and a concentration analysis for a certain sequence of dependent Bernoulli variables that may also be of independent interest. Because [Formula: see text] collapses to [Formula: see text] when there is no decay, it follows that having even the slightest bit of dependency (any [Formula: see text]) in the random graph construction leads to the presence of large independent sets, and thus, our random model has a phase transition at its boundary value of r = 1. This implies that there are large matchings in the line graph of [Formula: see text], which is a Markov random field. For the maximal independent set output by a greedy algorithm, we deduce that it has a performance ratio of at most [Formula: see text] w.h.p. when the lowest degree vertex is picked at each iteration and also show that, under any other permutation of vertices, the algorithm outputs a set of size [Formula: see text], where [Formula: see text] and, hence, has a performance ratio of [Formula: see text].Funding: The initial phase of this research was supported by the National Science Foundation [Grant DMS-1913294].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"17 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141609401","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

Order Independence in Sequential, Issue-by-Issue Voting 逐期顺序表决中的顺序独立性

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-12 DOI: 10.1287/moor.2022.0342

Alex Gershkov, Benny Moldovanu, Xianwen Shi

{"title":"Order Independence in Sequential, Issue-by-Issue Voting","authors":"Alex Gershkov, Benny Moldovanu, Xianwen Shi","doi":"10.1287/moor.2022.0342","DOIUrl":"https://doi.org/10.1287/moor.2022.0342","url":null,"abstract":"We study when the voting outcome is independent of the order of issues put up for vote in a spatial multidimensional voting model. Agents equipped with norm-based preferences that use a norm to measure the distance from their ideal policy vote sequentially and issue by issue via simple majority. If the underlying norm is generated by an inner product—such as the Euclidean norm—then the voting outcome is order independent if and only if the issues are orthogonal. If the underlying norm is a general one, then the outcome is order independent if the basis defining the issues to be voted upon satisfies the following property; for any vector in the basis, any linear combination of the other vectors is Birkhoff–James orthogonal to it. We prove a partial converse in the case of two dimensions; if the underlying basis fails this property, then the voting order matters. Finally, despite existence results for the two-dimensional case and for the general lp case, we show that nonexistence of bases with this property is generic.Funding: The research of A. Gershkov is supported by the Israel Science Foundation [Grant 1118/22]. The research of B. Moldovanu is supported by the German Science Foundation through the Hausdorff Center for Mathematics and The Collaborative Research Center Transregio 224. The research of X. Shi is supported by the Social Sciences and Humanities Research Council of Canada.","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"17 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614395","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

Rockafellian Relaxation and Stochastic Optimization Under Perturbations 扰动下的 Rockafellian 放松和随机优化

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-11 DOI: 10.1287/moor.2022.0122

Johannes O. Royset, Louis L. Chen, Eric Eckstrand

{"title":"Rockafellian Relaxation and Stochastic Optimization Under Perturbations","authors":"Johannes O. Royset, Louis L. Chen, Eric Eckstrand","doi":"10.1287/moor.2022.0122","DOIUrl":"https://doi.org/10.1287/moor.2022.0122","url":null,"abstract":"In practice, optimization models are often prone to unavoidable inaccuracies because of dubious assumptions and corrupted data. Traditionally, this placed special emphasis on risk-based and robust formulations, and their focus on “conservative” decisions. We develop, in contrast, an “optimistic” framework based on Rockafellian relaxations in which optimization is conducted not only over the original decision space but also jointly with a choice of model perturbation. The framework enables us to address challenging problems with ambiguous probability distributions from the areas of two-stage stochastic optimization without relatively complete recourse, probability functions lacking continuity properties, expectation constraints, and outlier analysis. We are also able to circumvent the fundamental difficulty in stochastic optimization that convergence of distributions fails to guarantee convergence of expectations. The framework centers on the novel concepts of exact and limit-exact Rockafellians, with interpretations of “negative” regularization emerging in certain settings. We illustrate the role of Phi-divergence, examine rates of convergence under changing distributions, and explore extensions to first-order optimality conditions. The main development is free of assumptions about convexity, smoothness, and even continuity of objective functions. Numerical results in the setting of computer vision and text analytics with label noise illustrate the framework.Funding: This work was supported by the Air Force Office of Scientific Research (Mathematical Optimization Program) under the grant: “Optimal Decision Making under Tight Performance Requirements in Adversarial and Uncertain Environments: Insight from Rockafellian Functions.”","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"14 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141614397","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

Investment Timing and Technological Breakthroughs 投资时机与技术突破

IF 1.7 3区数学

Mathematics of Operations Research Pub Date : 2024-07-09 DOI: 10.1287/moor.2022.0022

Jean-Paul Décamps, Fabien Gensbittel, Thomas Mariotti

{"title":"Investment Timing and Technological Breakthroughs","authors":"Jean-Paul Décamps, Fabien Gensbittel, Thomas Mariotti","doi":"10.1287/moor.2022.0022","DOIUrl":"https://doi.org/10.1287/moor.2022.0022","url":null,"abstract":"We study the optimal investment policy of a firm facing both technological and cash-flow uncertainty. At any point in time, the firm can irreversibly invest in a stand-alone technology or wait for a technological breakthrough. Breakthroughs occur when market conditions become favorable enough, exceeding a threshold value that is ex ante unknown to the firm. The Markov state variables for the optimal investment policy are the current market conditions and their historic maximum, and the firm optimally invests in the stand-alone technology only when market conditions deteriorate enough after reaching a maximum. The path-dependent return required for investing in the stand-alone technology is always higher than if no technological breakthroughs could occur and can take arbitrarily large values following certain histories. Decreases in development costs or increases in the value of the new technology make the firm more prone to bearing downside risk and delaying investment in the stand-alone technology.Funding: This research has benefited from financial support of the ANR [Programmes d’Investissements d’Avenir CHESS ANR-17-EURE-0010 and ANITI ANR-19-PI3A-0004] and the research foundation TSE-Partnership [Chaire Marchés des Risques et Création de Valeur, Fondation du Risque/SCOR].","PeriodicalId":49852,"journal":{"name":"Mathematics of Operations Research","volume":"40 1","pages":""},"PeriodicalIF":1.7,"publicationDate":"2024-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141568637","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

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":"25 1","pages":""},"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":"21 1","pages":""},"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