The value iteration algorithm in risk-sensitive average Markov decision chains with finite state space

• 成果类型: Article
• 署名作者: Cavazos-Cadena, R; Montes-de-Oca, R
• 署名单位: Universidad Autonoma Metropolitana - Mexico
• 刊物名称: MATHEMATICS OF OPERATIONS RESEARCH
• ISSN/ISSBN: 0364-765X
• DOI: 10.1287/moor.28.4.752.20515
• 发表日期: 2003
• 页码: 752-776
• 关键词: Discrete-time

摘要

This work concerns discrete-time Markov decision chains with finite state space and bounded costs. The controller has constant risk sensitivity A, and the performance of a control policy is measured by the corresponding risk-sensitive average cost criterion. Assuming that the optimality equation has a solution, it is shown that the value iteration scheme can be implemented to obtain, in a finite number of steps, (1) an approximation to the optimal A-sensitive average cost with an error less than a given tolerance, and (2) a stationary policy whose performance index is arbitrarily close to the optimal value. The argument used to establish these results is based on a modification of the original model, which is an extension of a transformation introduced by Schweitzer (1971) to analyze the the risk-neutral case.