Average Optimality of Markov Decision Processes with Unbounded Costs

Abstract

This paper considers Markov decision processes (MDPs) with Borel state space, not necessarily compact control constraint sets, and unbounded cost functions. The objective is to present some recent results on the existence of stationary optimal policies for MDPs with an average cost (AC) criterion. These results include extensions of recent works [7, 8, 9] based on the “vanishing discount factor” approach, as well as existence results for MDPs with strictly unbounded costs.