Average Cost Markov Decision Processes with Weakly Continuous Transition Probabilities

• 成果类型: Article
• 署名作者: Feinberg, Eugene A.; Kasyanov, Pavlo O.; Zadoianchuk, Nina V.
• 署名单位: State University of New York (SUNY) System; Stony Brook University; Ministry of Education & Science of Ukraine; Igor Sikorsky Kyiv Polytechnic Institute; National Academy of Sciences Ukraine; Institute for Applied System Analysis of the National Technical University of Ukraine Igor Sikorsky Kyiv Polytechnic Institute
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.1120.0555
• 发表日期: 2012
• 页码: 591-607
• 关键词: optimality; counterexample

摘要

This paper presents sufficient conditions for the existence of stationary optimal policies for average cost Markov decision processes with Borel state and action sets and weakly continuous transition probabilities. The one-step cost functions may be unbounded, and the action sets may be noncompact. The main contributions of this paper are: (i) general sufficient conditions for the existence of stationary discount optimal and average cost optimal policies and descriptions of properties of value functions and sets of optimal actions, (ii) a sufficient condition for the average cost optimality of a stationary policy in the form of optimality inequalities, and (iii) approximations of average cost optimal actions by discount optimal actions.