Maximizing the probability of visiting a set infinitely often for a Markov decision process with Borel state and action spaces

IF 0.7 4区 数学 Q3 STATISTICS & PROBABILITY
François Dufour, Tomás Prieto-Rumeau
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引用次数: 0

Abstract

We consider a Markov control model with Borel state space, metric compact action space, and transitions assumed to have a density function with respect to some probability measure satisfying some continuity conditions. We study the optimization problem of maximizing the probability of visiting some subset of the state space infinitely often, and we show that there exists an optimal stationary Markov policy for this problem. We endow the set of stationary Markov policies and the family of strategic probability measures with adequate topologies (namely, the narrow topology for Young measures and the $ws^\infty$ -topology, respectively) to obtain compactness and continuity properties, which allow us to obtain our main results.
最大化具有 Borel 状态和行动空间的马尔可夫决策过程无限次访问集合的概率
我们考虑了一个马尔可夫控制模型,该模型具有 Borel 状态空间、度量紧凑的行动空间,并假定过渡具有关于满足某些连续性条件的概率度量的密度函数。我们研究了最大化无限次访问状态空间某个子集的概率的优化问题,并证明了该问题存在最优的静态马尔可夫策略。我们为静态马尔可夫策略集和策略概率度量族赋予了适当的拓扑(即分别为杨度量的窄拓扑和 $ws^\infty$ -拓扑),从而获得了紧凑性和连续性特性,这使我们能够得到我们的主要结果。
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来源期刊
Journal of Applied Probability
Journal of Applied Probability 数学-统计学与概率论
CiteScore
1.50
自引率
10.00%
发文量
92
审稿时长
6-12 weeks
期刊介绍: Journal of Applied Probability is the oldest journal devoted to the publication of research in the field of applied probability. It is an international journal published by the Applied Probability Trust, and it serves as a companion publication to the Advances in Applied Probability. Its wide audience includes leading researchers across the entire spectrum of applied probability, including biosciences applications, operations research, telecommunications, computer science, engineering, epidemiology, financial mathematics, the physical and social sciences, and any field where stochastic modeling is used. A submission to Applied Probability represents a submission that may, at the Editor-in-Chief’s discretion, appear in either the Journal of Applied Probability or the Advances in Applied Probability. Typically, shorter papers appear in the Journal, with longer contributions appearing in the Advances.
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