Unifying On- and Off-Policy Variance Reduction Methods
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866917324988088320 |
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| author | Jeunen, Olivier |
| author_facet | Jeunen, Olivier |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2603_08370 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Unifying On- and Off-Policy Variance Reduction Methods Jeunen, Olivier Machine Learning Information Retrieval Methodology 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. |
| title | Unifying On- and Off-Policy Variance Reduction Methods |
| topic | Machine Learning Information Retrieval Methodology |
| url | https://arxiv.org/abs/2603.08370 |