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The average cost optimality is known to be a challenging problem forpartially observable stochastic control, with few results available beyond thefinite state, action, and measurement setup, for which somewhat restrictiveconditions are available. In this paper, we present explicit and easilytestable conditions for the existence of solutions to the average costoptimality equation where the state space is compact. In particular, we presenta new contraction based analysis, which is new to the literature to ourknowledge, building on recent regularity results for non-linear filters. Beyondestablishing existence, we also present several implications of our analysisthat are new to the literature: (i) robustness to incorrect priors (ii) nearoptimality of policies based on quantized approximations, (iii) near optimalityof policies with finite memory, and (iv) convergence in Q-learning. In additionto our main theorem, each of these represents a novel contribution for averagecost criteria.

Average Cost Optimality of Partially Observed MDPS: Contraction of Non-linear Filters, Optimal Solutions and Approximations