Mathematical Methods of Operations Research最新文献

Low-complexity algorithm for restless bandits with imperfect observations 观测不完善的不安定强盗的低复杂度算法

IF 1.2 4区数学

Mathematical Methods of Operations Research Pub Date : 2024-09-05 DOI: 10.1007/s00186-024-00868-x

Keqin Liu, Richard Weber, Chengzhong Zhang

{"title":"Low-complexity algorithm for restless bandits with imperfect observations","authors":"Keqin Liu, Richard Weber, Chengzhong Zhang","doi":"10.1007/s00186-024-00868-x","DOIUrl":"https://doi.org/10.1007/s00186-024-00868-x","url":null,"abstract":"We consider a class of restless bandit problems that finds a broad application area in reinforcement learning and stochastic optimization. We consider N independent discrete-time Markov processes, each of which had two possible states: 1 and 0 (‘good’ and ‘bad’). Only if a process is both in state 1 and observed to be so does reward accrue. The aim is to maximize the expected discounted sum of returns over the infinite horizon subject to a constraint that only M ((<N)) processes may be observed at each step. Observation is error-prone: there are known probabilities that state 1 (0) will be observed as 0 (1). From this one knows, at any time t, a probability that process i is in state 1. The resulting system may be modeled as a restless multi-armed bandit problem with an information state space of uncountable cardinality. Restless bandit problems with even finite state spaces are PSPACE-HARD in general. We propose a novel approach for simplifying the dynamic programming equations of this class of restless bandits and develop a low-complexity algorithm that achieves a strong performance and is readily extensible to the general restless bandit model with observation errors. Under certain conditions, we establish the existence (indexability) of Whittle index and its equivalence to our algorithm. When those conditions do not hold, we show by numerical experiments the near-optimal performance of our algorithm in the general parametric space. Furthermore, we theoretically prove the optimality of our algorithm for homogeneous systems.","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201491","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Multi-stage distributionally robust convex stochastic optimization with Bayesian-type ambiguity sets 具有贝叶斯型模糊集的多阶段分布稳健凸随机优化

IF 1.2 4区数学

Mathematical Methods of Operations Research Pub Date : 2024-08-14 DOI: 10.1007/s00186-024-00872-1

Wentao Ma, Zhiping Chen

{"title":"Multi-stage distributionally robust convex stochastic optimization with Bayesian-type ambiguity sets","authors":"Wentao Ma, Zhiping Chen","doi":"10.1007/s00186-024-00872-1","DOIUrl":"https://doi.org/10.1007/s00186-024-00872-1","url":null,"abstract":"The existent methods for constructing ambiguity sets in distributionally robust optimization often suffer from over-conservativeness and inefficient utilization of available data. To address these limitations and to practically solve multi-stage distributionally robust optimization (MDRO), we propose a data-driven Bayesian-type approach that constructs the ambiguity set of possible distributions from a Bayesian perspective. We demonstrate that our Bayesian-type MDRO problem can be reformulated as a risk-averse multi-stage stochastic programming problem and subsequently investigate its theoretical properties such as consistency, finite sample guarantee, and statistical robustness. Moreover, the reformulation enables us to employ cutting planes algorithms in dynamic settings to solve the Bayesian-type MDRO problem. To illustrate the practicality and advantages of the proposed model and algorithm, we apply it to a distributionally robust inventory control problem and a distributionally robust hydrothermal scheduling problem, and compare it with usual formulations and solution methods to highlight the superior performance of our approach.","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"15 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-08-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142201492","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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 new value for communication situations 交流情况的新价值

IF 1.2 4区数学

Mathematical Methods of Operations Research Pub Date : 2024-08-12 DOI: 10.1007/s00186-024-00873-0

Daniel Li Li, Erfang Shan

引用次数: 0

On the relationship between the value function and the efficient frontier of a mixed integer linear optimization problem 论混合整数线性优化问题的价值函数与有效前沿之间的关系

IF 1.2 4区数学

Mathematical Methods of Operations Research Pub Date : 2024-08-02 DOI: 10.1007/s00186-024-00871-2

Samira Fallah, Ted K. Ralphs, Natashia L. Boland

{"title":"On the relationship between the value function and the efficient frontier of a mixed integer linear optimization problem","authors":"Samira Fallah, Ted K. Ralphs, Natashia L. Boland","doi":"10.1007/s00186-024-00871-2","DOIUrl":"https://doi.org/10.1007/s00186-024-00871-2","url":null,"abstract":"In this study, we investigate the connection between the efficient frontier (EF) of a general multiobjective mixed integer linear optimization problem (MILP) and the so-called restricted value function (RVF) of a closely related single-objective MILP. In the first part of the paper, we detail the mathematical structure of the RVF, including characterizing the set of points at which it is differentiable, the gradients at such points, and the subdifferential at all nondifferentiable points. We then show that the EF of the multiobjective MILP is comprised of points on the boundary of the epigraph of the RVF and that any description of the EF suffices to describe the RVF and vice versa. Because of the close relationship of the RVF to the EF, we observe that methods for constructing the so-called value function (VF) of an MILP and methods for constructing the EF of a multiobjective optimization problem are effectively interchangeable. Exploiting this observation, we propose a generalized cutting-plane algorithm for constructing the EF of a multiobjective MILP that arises from an existing algorithm for constructing the classical MILP VF. The algorithm identifies the set of all integer parts of solutions on the EF. We prove that the algorithm converges finitely under a standard boundedness assumption and comes with a performance guarantee if terminated early.","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"56 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-08-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141880569","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

An approximation algorithm for multiobjective mixed-integer convex optimization 多目标混合整数凸优化的近似算法

IF 1.2 4区数学

Mathematical Methods of Operations Research Pub Date : 2024-07-29 DOI: 10.1007/s00186-024-00870-3

Ina Lammel, Karl-Heinz Küfer, Philipp Süss

引用次数: 0

Tropical convexity in location problems 位置问题中的热带凸性

IF 1.2 4区数学

Mathematical Methods of Operations Research Pub Date : 2024-07-03 DOI: 10.1007/s00186-024-00869-w

Andrei Comăneci

引用次数: 0

Discrete-time stopping games with risk-sensitive discounted cost criterion 具有风险敏感贴现成本标准的离散时间停止博弈

IF 1.2 4区数学

Mathematical Methods of Operations Research Pub Date : 2024-07-02 DOI: 10.1007/s00186-024-00864-1

Wenzhao Zhang, Congying Liu

引用次数: 0

Convex optimization via inertial algorithms with vanishing Tikhonov regularization: fast convergence to the minimum norm solution 通过惯性算法的凸优化与消失的 Tikhonov 正则化：快速收敛至最小规范解

IF 1.2 4区数学

Mathematical Methods of Operations Research Pub Date : 2024-06-27 DOI: 10.1007/s00186-024-00867-y

Hedy Attouch, Szilárd Csaba László

{"title":"Convex optimization via inertial algorithms with vanishing Tikhonov regularization: fast convergence to the minimum norm solution","authors":"Hedy Attouch, Szilárd Csaba László","doi":"10.1007/s00186-024-00867-y","DOIUrl":"https://doi.org/10.1007/s00186-024-00867-y","url":null,"abstract":"In a Hilbertian framework, for the minimization of a general convex differentiable function f, we introduce new inertial dynamics and algorithms that generate trajectories and iterates that converge fastly towards the minimizer of f with minimum norm. Our study is based on the non-autonomous version of the Polyak heavy ball method, which, at time t, is associated with the strongly convex function obtained by adding to f a Tikhonov regularization term with vanishing coefficient (varepsilon (t)). In this dynamic, the damping coefficient is proportional to the square root of the Tikhonov regularization parameter (varepsilon (t)). By adjusting the speed of convergence of (varepsilon (t)) towards zero, we will obtain both rapid convergence towards the infimal value of f, and the strong convergence of the trajectories towards the element of minimum norm of the set of minimizers of f. In particular, we obtain an improved version of the dynamic of Su-Boyd-Candès for the accelerated gradient method of Nesterov. This study naturally leads to corresponding first-order algorithms obtained by temporal discretization. In the case of a proper lower semicontinuous and convex function f, we study the proximal algorithms in detail, and show that they benefit from similar properties.\u0000","PeriodicalId":49862,"journal":{"name":"Mathematical Methods of Operations Research","volume":"196 1","pages":""},"PeriodicalIF":1.2,"publicationDate":"2024-06-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141509496","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"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

Asymptotic upper bounds for an M/M/C/K retrial queue with a guard channel and guard buffer 带保护通道和保护缓冲区的 M/M/C/K 重审队列的渐近上限

IF 1.2 4区数学

Mathematical Methods of Operations Research Pub Date : 2024-06-26 DOI: 10.1007/s00186-024-00865-0

Nesrine Zidani, Natalia Djellab

引用次数: 0

Convergence rate of LQG mean field games with common noise 具有共同噪声的 LQG 平均场博弈的收敛率

IF 1.2 4区数学

Mathematical Methods of Operations Research Pub Date : 2024-06-25 DOI: 10.1007/s00186-024-00863-2

Jiamin Jian, Qingshuo Song, Jiaxuan Ye

引用次数: 0