期刊论文详细信息
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS 卷:396
Average control of Markov decision processes with Feller transition probabilities and general action spaces
Article
Costa, O. L. V.2  Dufour, F.1 
[1] Univ Bordeaux, Inst Math Bordeaux, INRIA Bordeaux Sud Ouest, IMB,Team CQFD, F-33405 Talence, France
[2] Univ Sao Paulo, Dept Engn Telecomunicacoes & Controle, Escola Politecn, BR-05508900 Sao Paulo, Brazil
关键词: Markov Decision Processes;    Average cost;    General Borel spaces;    Feller transition probabilities;    Non-compact action set;    Policy iteration;   
DOI  :  10.1016/j.jmaa.2012.05.073
来源: Elsevier
PDF
【 摘 要 】

This paper studies the average control problem of discrete-time Markov Decision Processes (MDPs for short) with general state space, Feller transition probabilities, and possibly non-compact control constraint sets A(x). Two hypotheses are considered: either the cost function c is strictly unbounded or the multifunctions A(r)(x) = {a is an element of A(x) : c(x, a) <= r} are upper-semicontinuous and compact-valued for each real r. For these two cases we provide new results for the existence of a solution to the average-cost optimality equality and inequality using the vanishing discount approach. We also study the convergence of the policy iteration approach under these conditions. It should be pointed out that we do not make any assumptions regarding the convergence and the continuity of the limit function generated by the sequence of relative difference of the alpha-discounted value functions and the Poisson equations as often encountered in the literature. (C) 2012 Elsevier Inc. All rights reserved.

【 授权许可】

Free   

【 预 览 】
附件列表
Files Size Format View
10_1016_j_jmaa_2012_05_073.pdf 285KB PDF download
  文献评价指标  
  下载次数:3次 浏览次数:0次