Nonstationary denumerable state Markov decision processes – with average variance criterion

In this paper, we consider the nonstationary Markov decision processes with average variance criterion on a countable state space, finite action spaces and bounded one-step rewards. From the optimality equations which are provided in this paper, we translate the average variance criterion into a new average expected cost criterion. Then we prove that there exists a Markov policy, which is optimal in an original average expected reward criterion, that minimizes the average variance in the class of optimal policies for the original average expected reward criterion.