A Counterexample on Sample-Path Optimality in Stable Markov Decision Chains with the Average Reward Criterion

Abstract

This note deals with Markov decision chains evolving on a denumerable state space. Under standard continuity-compactness requirements, an explicit example is provided to show that, with respect to a strong sample-path average reward criterion, the Lyapunov function condition does not ensure the existence of an optimal stationary policy.