Solutions of the average cost optimality equation for Markov decision processes with weakly continuous kernel: The fixed-point approach revisited

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:464

Article

Vega-Amaya, Oscar^1,2 

[1] Univ Sonora, Dept Matemat, Hermosillo, Sonora, Mexico

[2] Luis Encinas & Rosales S-N, Hermosillo 83000, Sonora, Mexico

关键词: Markov decision processes;    Average cost optimality equation;    Lyapunov stability condition;    Banach fixed-point theorem;   

DOI  :  10.1016/j.jmaa.2018.03.077

来源: Elsevier

【 摘 要 】

This paper shows the existence of lower semicontinuous solutions of the average cost optimality equation for Markov decision processes with Borel spaces, possible unbounded cost function and weakly continuous transition kernel. This is done imposing a growth condition on the cost function, a Lyapunov stability condition on the transition kernel and a set of standard compactness-continuity conditions. The solution of the average cost optimality equation is obtained by means of the Banach fixed-point theorem. (C) 2018 Elsevier Inc. All rights reserved.

【 授权许可】

Free