Non-ergodic Markov decision processes with a constraint on the asymptotic failure rate: general class of policies

In this paper, we introduce a Markov decision model with absorbing states and a constraint on the asymptotic failure rate. The objective is to find a policy which maximizes the infinite horizon expected average reward, given that the system never fails. First, we show that it is sufficient to consider markovian policies. Second, for solving the problem, we restrict ourselves to find a stationary policy. Finally, we give sufficient conditions for optimality in the Markovian policies class.