# Unifying On- and Off-Policy Variance Reduction Methods

arXiv: https://arxiv.org/abs/2603.08370 · HTML: https://mlsanity.com/paper/2603.08370/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 9 Mar 2026.

## Builds on (most cited first, 12 of 12)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Doubly Robust Policy Evaluation and Optimization](https://mlsanity.com/paper/1503.02834/) (2015)
- [More Robust Doubly Robust Off-policy Evaluation](https://mlsanity.com/paper/1802.03493/) (2018)
- [Offline A/B testing for Recommender Systems](https://mlsanity.com/paper/1801.07030/) (2018)
- [Machine Learning for Variance Reduction in Online Experiments](https://mlsanity.com/paper/2106.07263/) (2021)
- [Optimal Baseline Corrections for Off-Policy Contextual Bandits](https://mlsanity.com/paper/2405.05736/) (2024)
- [Correcting for Interference in Experiments: A Case Study at Douyin](https://mlsanity.com/paper/2305.02542/) (2023)
- [Delta-rm OPE: Off-Policy Estimation with Pairs of Policies](https://mlsanity.com/paper/2405.10024/) (2024)
- [Variance Reduction in Ratio Metrics for Efficient Online Experiments](https://mlsanity.com/paper/2401.04062/) (2024)
- [A Common Misassumption in Online Experiments with Machine Learning Models](https://mlsanity.com/paper/2304.10900/) (2023)
- [Powerful A/B-Testing Metrics and Where to Find Them](https://mlsanity.com/paper/2407.20665/) (2024)
- [Additive Control Variates Dominate Self-Normalisation in Off-Policy Evaluation](https://mlsanity.com/paper/2602.14914/) (2026)

## Built on by (most cited first, 1 of 1)

- [Accelerating A/B-Tests with Counterfactual Estimation: Reducing Variance through Policy Overlap](https://mlsanity.com/paper/2607.14604/) (2026)

## Abstract (arXiv)

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.