UVIP: Model-Free Approach to Evaluate Reinforcement Learning Algorithms

TL;DR

This paper introduces UVIP, a model-free method for evaluating how far a policy is from optimal in reinforcement learning, providing upper bounds and confidence intervals for the optimal value.

Contribution

The paper proposes UVIP, a novel model-free upper value iteration method that estimates the suboptimality gap and constructs confidence intervals for the optimal value in RL.

Findings

UVIP provides reliable upper bounds on the suboptimality gap.

Theoretical guarantees are established for UVIP under general conditions.

Performance demonstrated on benchmark RL problems.

Abstract

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 $V^{\pi}$ corresponding to a policy $\pi$ does not provide reliable information on how far the policy $\pi$ 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 $V^{\star}(x) - V^{\pi}(x)$ 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 the martingale approach. We provide theoretical guarantees for {\sf UVIP} under general assumptions and illustrate its performance on a number of benchmark RL problems.