UVIP: Model-Free Approach to Evaluate Reinforcement Learning Algorithms

Policy evaluation is an important instrument for the comparison of different algorithms in Reinforcement Learning (RL). However, even a precise knowledge of the value function Vπ corresponding to a policy π does not provide reliable information on how far the policy π is from the optimal one. We present a novel model-free upper value iteration procedure (sf UVIP) that allows us to estimate the suboptimality gap Vstar(x) - Vπ(x) from above and to construct confidence intervals for (V^star). Our approach relies on upper bounds to the solution of the Bellman optimality equation via the martingale approach. We provide theoretical guarantees for sf UVIP under general assumptions and illustrate its performance on a number of benchmark RL problems.