Existence of optimal stationary policies in average reward Markov decision processes with a recurrent state

Abstract

We consider discrete-timeaverage reward Markov decision processes with denumerable state space andbounded reward function. Under structural restrictions on the model the existence of an optimal stationary policy is proved; both the lim inf and lim sup average criteria are considered. In contrast to the usual approach our results donot rely on the average regard optimality equation. Rather, the arguments are based on well-known facts fromRenewal Theory.