{"title":"Risk-Sensitive Average Markov Decision Processes in General Spaces","authors":"Xian Chen, Qingda Wei","doi":"10.1137/23m156118x","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Control and Optimization, Volume 62, Issue 4, Page 2115-2147, August 2024. <br/> 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.","PeriodicalId":49531,"journal":{"name":"SIAM Journal on Control and Optimization","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Control and Optimization","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m156118x","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"AUTOMATION & CONTROL SYSTEMS","Score":null,"Total":0}
引用次数: 0
Abstract
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.
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.
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