Title: Maximizing the probability of visiting a set infinitely often for a countable state space Markov decision process

Abstract: This is a joint work with Tomas Prieto-Rumeau. In this talk, we consider a Markov decision process with countable state space and Borel action space. We are interested in maximizing the probability that the controlled Markov chain visits some subset of the state space infinitely often. We provide sufficient conditions, based on continuity and compactness requirements, together with a stability condition on a parametrized family of auxiliary control models, which imply the existence of a deterministic stationary optimal policy. We compare our hypotheses with those existing in the literature.