一般空间中的风险敏感平均马尔可夫决策过程

IF 2.2 2区数学 Q2 AUTOMATION & CONTROL SYSTEMS

SIAM Journal on Control and Optimization Pub Date : 2024-07-12 DOI:10.1137/23m156118x

Xian Chen, Qingda Wei

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引用次数: 0

摘要

SIAM 控制与优化期刊》第 62 卷第 4 期第 2115-2147 页，2024 年 8 月。摘要本文研究在风险敏感平均成本准则下具有 Borel 状态和行动空间的离散时间马尔可夫决策过程。成本函数可以是无界的。我们引入了一个新的核，并证明了核的准紧凑性，由此导出了乘法泊松方程。此外，我们还开发了一种新方法来证明对风险敏感的平均成本最优方程的解的存在性，并得到最优确定性静态策略的存在性。此外，我们还举了两个例子来说明我们的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Risk-Sensitive Average Markov Decision Processes in General Spaces

SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 2115-2147, August 2024.
Abstract. In this paper we study discrete-time Markov decision processes with Borel state and action spaces under the risk-sensitive average cost criterion. The cost function can be unbounded. We introduce a new kernel and prove the quasi-compactness of the kernel from which the multiplicative Poisson equation is derived. Moreover, we develop a new approach to show the existence of a solution to the risk-sensitive average cost optimality equation and obtain the existence of an optimal deterministic stationary policy. Furthermore, we give two examples to illustrate our results.

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来源期刊

SIAM Journal on Control and Optimization 数学-应用数学

CiteScore

4.00

自引率

4.50%

发文量

143

审稿时长

12 months

期刊介绍： SIAM Journal on Control and Optimization (SICON) publishes original research articles on the mathematics and applications of control theory and certain parts of optimization theory. Papers considered for publication must be significant at both the mathematical level and the level of applications or potential applications. Papers containing mostly routine mathematics or those with no discernible connection to control and systems theory or optimization will not be considered for publication. From time to time, the journal will also publish authoritative surveys of important subject areas in control theory and optimization whose level of maturity permits a clear and unified exposition. The broad areas mentioned above are intended to encompass a wide range of mathematical techniques and scientific, engineering, economic, and industrial applications. These include stochastic and deterministic methods in control, estimation, and identification of systems; modeling and realization of complex control systems; the numerical analysis and related computational methodology of control processes and allied issues; and the development of mathematical theories and techniques that give new insights into old problems or provide the basis for further progress in control theory and optimization. Within the field of optimization, the journal focuses on the parts that are relevant to dynamic and control systems. Contributions to numerical methodology are also welcome in accordance with these aims, especially as related to large-scale problems and decomposition as well as to fundamental questions of convergence and approximation.