<p>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 <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$V^{\pi }$</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>V</mi> <mi>π</mi> </msup> </math></EquationSource> </InlineEquation> corresponding to a policy <InlineEquation ID="IEq2"> <EquationSource Format="TEX">$\pi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>π</mi> </math></EquationSource> </InlineEquation> does not provide reliable information on how far the policy <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$\pi $</EquationSource> <EquationSource Format="MATHML"><math> <mi>π</mi> </math></EquationSource> </InlineEquation> is from the optimal one. We present a novel model-free upper value iteration procedure (<Emphasis FontCategory="SansSerif">UVIP</Emphasis>) that allows us to estimate the suboptimality gap <InlineEquation ID="IEq4"> <EquationSource Format="TEX">$V^{\star }(x) - V^{\pi }(x)$</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>V</mi> <mo>⋆</mo> </msup> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> <mo>-</mo> <msup> <mi>V</mi> <mi>π</mi> </msup> <mrow> <mo stretchy="false">(</mo> <mi>x</mi> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> from above and to construct confidence intervals for <InlineEquation ID="IEq5"> <EquationSource Format="TEX">$V^\star $</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mi>V</mi> <mo>⋆</mo> </msup> </math></EquationSource> </InlineEquation>. Our approach relies on upper bounds to the solution of the Bellman optimality equation via the martingale approach. We provide theoretical guarantees for <Emphasis FontCategory="SansSerif">UVIP</Emphasis> under general assumptions and illustrate its performance on a number of benchmark RL problems. Communicated by Alexander Vladimirovich Gasnikov.</p>

UVIP: Model-Free Approach to Evaluate Reinforcement Learning Algorithms

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发表日期：

2026年2月3日

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Denis Belomestny,
Ilya Levin,
Alexey Naumov,
Sergey Samsonov

摘要

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 $V^{\pi }$ $V^{π}$ corresponding to a policy $\pi $ $π$ does not provide reliable information on how far the policy $\pi $ $π$ is from the optimal one. We present a novel model-free upper value iteration procedure (UVIP) that allows us to estimate the suboptimality gap $V^{\star }(x) - V^{\pi }(x)$ $V^{⋆} (x) - V^{π} (x)$ from above and to construct confidence intervals for $V^\star $ $V^{⋆}$ . Our approach relies on upper bounds to the solution of the Bellman optimality equation via the martingale approach. We provide theoretical guarantees for UVIP under general assumptions and illustrate its performance on a number of benchmark RL problems. Communicated by Alexander Vladimirovich Gasnikov.