# Double Clipping: Less-Biased Variance Reduction in Off-Policy Evaluation

arXiv: https://arxiv.org/abs/2309.01120 · HTML: https://mlsanity.com/paper/2309.01120/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 20 references that are in the map.
- First posted on arXiv 3 Sep 2023.

## Builds on (most cited first, 9 of 9)

- [Unbiased Learning-to-Rank with Biased Feedback](https://mlsanity.com/paper/1608.04468/) (2016)
- [Optimal and Adaptive Off-policy Evaluation in Contextual Bandits](https://mlsanity.com/paper/1612.01205/) (2016)
- [Off-policy evaluation for slate recommendation](https://mlsanity.com/paper/1605.04812/) (2016)
- [Doubly robust off-policy evaluation with shrinkage](https://mlsanity.com/paper/1907.09623/) (2019)
- [Adaptive Estimator Selection for Off-Policy Evaluation](https://mlsanity.com/paper/2002.07729/) (2020)
- [Offline Evaluation of Ranking Policies with Click Models](https://mlsanity.com/paper/1804.10488/) (2018)
- [Policy-Adaptive Estimator Selection for Off-Policy Evaluation](https://mlsanity.com/paper/2211.13904/) (2022)
- [Doubly-Robust Estimation for Correcting Position-Bias in Click Feedback for Unbiased Learning to Rank](https://mlsanity.com/paper/2203.17118/) (2022)
- [Off-policy evaluation for learning-to-rank via interpolating the item-position model and the position-based model](https://mlsanity.com/paper/2210.09512/) (2022)

## Built on by (most cited first, 2 of 2)

- [Off-Policy Evaluation and Learning for Matching Markets](https://mlsanity.com/paper/2507.13608/) (2025)
- [Meta Off-Policy Estimation](https://mlsanity.com/paper/2508.07914/) (2025)

## Abstract (arXiv)

"Clipping" (a.k.a. importance weight truncation) is a widely used variance-reduction technique for counterfactual off-policy estimators. Like other variance-reduction techniques, clipping reduces variance at the cost of increased bias. However, unlike other techniques, the bias introduced by clipping is always a downward bias (assuming non-negative rewards), yielding a lower bound on the true expected reward. In this work we propose a simple extension, called textitdouble clipping, which aims to compensate this downward bias and thus reduce the overall bias, while maintaining the variance reduction properties of the original estimator.