Bias optimality and strong n (n =-1, 0) discount optimality for Markov decision processes

摘要

In this paper we study both bias optimality and strong n (n = -1,0) discount optimality for denumerable discrete-time Markov decision processes. The rewards may have neither upper not lower bounds. We give sufficient conditions on the system's primitive data, and under which we prove (1) the existence of the bias optimality equation and bias optimal policies; (2) a condition equivalent to bias optimal policies; (3) average expected reward optintality and strong -1-discount optirnality are equivalent; (4) bias optimality and strong 0-discount optirnality are equivalent; (5) the existence of strong n (n = -1,0) discount optimal stationary policies. Our conditions are weaker than those in the previous literature. Moreover, our results are illustrated by a controlled random walk. (c) 2007 Elsevier Inc. All rights reserved.