Paper ID: 2105.02135

UVIP: Model-Free Approach to Evaluate Reinforcement Learning Algorithms

Ilya Levin, Denis Belomestny, Alexey Naumov, Sergey Samsonov

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.

Submitted: May 5, 2021