Deviation Matrix, Laurent Series and Blackwell Optimality in Countable State Markov Decision Processes

Abstract

This paper presents a recurrent condition on Markov decision processes with a countable state space and bounded rewards. The condition is sufficient for the existence of a Blackwell optimal stationary policy, having the Laurent series expansion with continuous coefficients. It is so relaxed that the Markov chain corresponding to a stationary policy may have countably many periodic recurrent classes. Our method finds the deviation matrix in an explicit form.