DISCOUNTED CONTINUOUS-TIME CONSTRAINED MARKOV DECISION PROCESSES IN POLISH SPACES

• 成果类型: Article
• 署名作者: Guo, Xianping; Song, Xinyuan
• 署名单位: Sun Yat Sen University; Chinese University of Hong Kong
• 刊物名称: ANNALS OF APPLIED PROBABILITY
• ISSN/ISSBN: 1050-5164
• DOI: 10.1214/10-AAP749
• 发表日期: 2011
• 页码: 2016-2049
• 关键词: bias optimality; countable state; policies; models

摘要

This paper is devoted to studying constrained continuous-time Markov decision processes (MDPs) in the class of randomized policies depending on state histories. The transition rates may be unbounded, the reward and costs are admitted to be unbounded from above and from below, and the state and action spaces are Polish spaces. The optimality criterion to be maximized is the expected discounted rewards, and the constraints can be imposed on the expected discounted costs. First, we give conditions for the nonexplosion of underlying processes and the finiteness of the expected discounted rewards/costs. Second, using a technique of occupation measures, we prove that the constrained optimality of continuous-time MDPs can be transformed to an equivalent (optimality) problem over a class of probability measures. Based on the equivalent problem and a so-called (w) over bar -weak convergence of probability measures developed in this paper, we show the existence of a constrained optimal policy. Third, by providing a linear programming formulation of the equivalent problem, we show the solvability of constrained optimal policies. Finally, we use two computable examples to illustrate our main results.