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## 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). Yet even a precise knowledge of the value function $V^{\pi}$ corresponding to a policy $\pi$ does not provide reliable information on how far is the  policy $\pi$ from the optimal one. We present a novel model-free upper value iteration procedure ({\sf UVIP}) that allows us to estimate the suboptimality gap $V^{\star}(x) - V^{\pi}(x)$ 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 martingale approach. We provide theoretical guarantees for {\sf UVIP} under general assumptions and illustrate its performance on a number of benchmark RL problems.