Policy Iteration for Continuous-Time Average Reward Markov Decision Processes in Polish Spaces

We study thepolicy iteration algorithm(PIA) for continuous-time jump Markov decision processes in general state and action spaces. The corresponding transition rates are allowed to beunbounded, and the reward rates may haveneither upper nor lower bounds. The criterion that we are concerned with isexpected average reward. We propose a set of conditions under which we first establish the average reward optimality equation and present the PIA. Then under twoslightlydifferent sets of conditions we show that the PIA yields the optimal (maximum) reward, an average optimal stationary policy, and a solution to the average reward optimality equation.