UVIP: Model-Free Approach to Evaluate Reinforcement Learning Algorithms

Working papers by Cornell University. Series math "arxiv.org". 2021. Article 2105.02135.

Belomestny D., Levin I., Moulines E., Naumov A., Samsonov S., Zorina V.

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.

Keywords: policy evaluation, policy error, confidence intervals for optimal value function

Publication based on the results of: Uncertainty quantification in machine learning algorithms (2021)