Average-Cost Markov Decision Processes with Weakly Continuous Transition Probabilities

This paper presents sufficient conditions for the existence of stationary optimal policies for average-cost Markov Decision Processes with Borel state and action sets and with weakly continuous transition probabilities. The one-step cost functions may be unbounded, and action sets may be noncompact. The main contributions of this paper are: (i) general sufficient conditions for the existence of stationary discount-optimal and average-cost optimal policies and descriptions of properties of value functions and sets of optimal actions, (ii) a sufficient condition for the average-cost optimality of a stationary policy in the form of optimality inequalities, and (iii) approximations of average-cost optimal actions by discount-optimal actions.