Unifying On- and Off-Policy Variance Reduction Methods

Olivier Jeunen

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arXiv · 2603.08370

Unifying On- and Off-Policy Variance Reduction Methods

Olivier Jeunen

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Abstract

Continuous and efficient experimentation is key to the practical success of user-facing applications on the web, both through online A/B-tests and off-policy evaluation. Despite their shared objective -- estimating the incremental value of a treatment -- these domains often operate in isolation, utilising distinct terminologies and statistical toolkits. This paper bridges that divide by establishing a formal equivalence between their canonical variance reduction methods. We prove that the standard online Difference-in-Means estimator is mathematically identical to an off-policy Inverse Propensity Scoring estimator equipped with an optimal (variance-minimising) additive control variate. Extending this unification, we demonstrate that widespread regression adjustment methods (such as CUPED, CUPAC, and ML-RATE) are structurally equivalent to Doubly Robust estimation. This unified view extends our understanding of commonly used approaches, and can guide practitioners and researchers working on either class of problems.

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Olivier Jeunen. 2026-03-09. Unifying On- and Off-Policy Variance Reduction Methods. https://arxiv.org/abs/2603.08370

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