Offline Actor-Critic for Average Reward MDPs

We study offline policy optimization for infinite-horizon average-reward Markov decision processes (MDPs) with large or infinite state spaces. Specifically, we propose a pessimistic version of actor-critic methods using a computationally efficient linear function class for value function estimation. At the core of our method is a critic that computes a pessimistic estimate of the average reward under the current policy, as well as the corresponding policy gradient, by solving a fixedpoint Bellman equation, rather than solving a successive sequence of regression problems as in finite horizon settings. Due to the nature of our policy-based method, the critic only needs to solve a linear optimization problem with convex quadratic constraints. We show that a very mild data coverage requirement is sufficient for our algorithm to achieve O(ε 2) sample complexity for learning a near-optimal policy up to model misspecification errors. To our knowledge, this is the first result with optimal εdependence in the offline average reward setting.