On Linear Programming for Constrained and Unconstrained Average-Cost Markov Decision Processes with Countable Action Spaces and Strictly Unbounded Costs

We consider the linear programming approach for constrained and unconstrained Markov decision processes (MDPs) under long-run average-cost criterion, where class of MDPs in our study have Borel state spaces discrete countable action spaces. Under a strict unboundedness condition on one-stage costs recently introduced majorization transition stochastic kernel, we infinite-dimensional programs prove absence duality gap other optimality results. Our results do not require lower-semicontinuous MDP model. Thus, they can be applied to space dynamics are discontinuous variable. proofs make use continuity property measurable functions asserted by Lusin’s theorem.