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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 contraction based analysis, which is new to the literature to our knowledge,building on recent regularity results for non-linear filters.

Average Cost Optimality of Partially Observed MDPs: Contraction of Non-linear Filters and Existence of Optimal Solutions