Performance of NPG in Countable State-Space Average-Cost RL

We consider policy optimization methods in reinforcement learning settings where the state space is arbitrarily large, or even countably infinite. The motivation arises from control problems in communication networks, matching markets, and other queueing systems. We consider Natural Policy Gradient (NPG), which is a popular algorithm for finite state spaces. Under reasonable assumptions, we derive a performance bound for NPG that is independent of the size of the state space, provided the error in policy evaluation is within a factor of the true value function. We obtain this result by establishing new policy-independent bounds on the solution to Poisson's equation, i.e., the relative value function, and by combining these bounds with previously known connections between MDPs and learning from experts.