# Doubly-Robust Estimation for Correcting Position-Bias in Click Feedback for Unbiased Learning to Rank

arXiv: https://arxiv.org/abs/2203.17118 · HTML: https://mlsanity.com/paper/2203.17118/

## Key facts

- Cited by 18 papers in the map (data through 14 Oct 2026).
- Builds on 24 of its 58 references that are in the map.
- First posted on arXiv 31 Mar 2022.

## Builds on (most cited first, 24 of 24)

- [Fairness of Exposure in Rankings](https://mlsanity.com/paper/1802.07281/) (2018)
- [Doubly Robust Policy Evaluation and Optimization](https://mlsanity.com/paper/1503.02834/) (2015)
- [Unbiased Learning-to-Rank with Biased Feedback](https://mlsanity.com/paper/1608.04468/) (2016)
- [Introducing LETOR 4.0 Datasets](https://mlsanity.com/paper/1306.2597/) (2013)
- [Unbiased Recommender Learning from Missing-Not-At-Random Implicit Feedback](https://mlsanity.com/paper/1909.03601/) (2019)
- [Policy Learning for Fairness in Ranking](https://mlsanity.com/paper/1902.04056/) (2019)
- [Optimal Regret Analysis of Thompson Sampling in Stochastic Multi-armed Bandit Problem with Multiple Plays](https://mlsanity.com/paper/1506.00779/) (2015)
- [Beyond the Selected Completely At Random Assumption for Learning from Positive and Unlabeled Data](https://mlsanity.com/paper/1809.03207/) (2018)
- [Computationally Efficient Optimization of Plackett-Luce Ranking Models for Relevance and Fairness](https://mlsanity.com/paper/2105.00855/) (2021)
- [Correcting for Selection Bias in Learning-to-rank Systems](https://mlsanity.com/paper/2001.11358/) (2020)
- [Offline Evaluation of Ranking Policies with Click Models](https://mlsanity.com/paper/1804.10488/) (2018)
- [Estimating Position Bias without Intrusive Interventions](https://mlsanity.com/paper/1812.05161/) (2018)
- [Doubly Robust Off-Policy Evaluation for Ranking Policies under the Cascade Behavior Model](https://mlsanity.com/paper/2202.01562/) (2022)
- [Multiple-Play Bandits in the Position-Based Model](https://mlsanity.com/paper/1606.02448/) (2016)
- [Differentiable Unbiased Online Learning to Rank](https://mlsanity.com/paper/1809.08415/) (2018)
- [Cascade Model-based Propensity Estimation for Counterfactual Learning to Rank](https://mlsanity.com/paper/2005.11938/) (2020)
- [Unifying Online and Counterfactual Learning to Rank](https://mlsanity.com/paper/2012.04426/) (2020)
- [Intervention Harvesting for Context-Dependent Examination-Bias Estimation](https://mlsanity.com/paper/1811.01802/) (2018)
- [Safe Exploration for Optimizing Contextual Bandits](https://mlsanity.com/paper/2002.00467/) (2020)
- [StochasticRank: Global Optimization of Scale-Free Discrete Functions](https://mlsanity.com/paper/2003.02122/) (2020)
- [Non-Clicks Mean Irrelevant? Propensity Ratio Scoring As a Correction](https://mlsanity.com/paper/2005.08480/) (2020)
- [Unbiased Learning to Rank: Online or Offline?](https://mlsanity.com/paper/2004.13574/) (2020)
- [Robust Generalization and Safe Query-Specialization in Counterfactual Learning to Rank](https://mlsanity.com/paper/2102.05990/) (2021)
- [Optimizing Ranking Models in an Online Setting](https://mlsanity.com/paper/1901.10262/) (2019)

## Built on by (most cited first, 18 of 18)

- [On (Normalised) Discounted Cumulative Gain as an Off-Policy Evaluation Metric for Top-n Recommendation](https://mlsanity.com/paper/2307.15053/) (2023)
- [Debiased Recommendation with Noisy Feedback](https://mlsanity.com/paper/2406.17182/) (2024)
- [Practical and Robust Safety Guarantees for Advanced Counterfactual Learning to Rank](https://mlsanity.com/paper/2407.19943/) (2024)
- [PRECISE: Reducing the Bias of LLM Evaluations Using Prediction-Powered Ranking Estimation](https://mlsanity.com/paper/2601.18777/) (2026)
- [Unified Off-Policy Learning to Rank: a Reinforcement Learning Perspective](https://mlsanity.com/paper/2306.07528/) (2023)
- [Identifiability Matters: Revealing the Hidden Recoverable Condition in Unbiased Learning to Rank](https://mlsanity.com/paper/2309.15560/) (2023)
- [Double Clipping: Less-Biased Variance Reduction in Off-Policy Evaluation](https://mlsanity.com/paper/2309.01120/) (2023)
- [Recent Advances in the Foundations and Applications of Unbiased Learning to Rank](https://mlsanity.com/paper/2305.02914/) (2023)
- [Investigating the Robustness of Counterfactual Learning to Rank Models: A Reproducibility Study](https://mlsanity.com/paper/2404.03707/) (2024)
- [Proximal Ranking Policy Optimization for Practical Safety in Counterfactual Learning to Rank](https://mlsanity.com/paper/2409.09881/) (2024)
- [A Control Function Framework for Mitigating Position Bias in Learning to Rank Systems](https://mlsanity.com/paper/2506.06989/) (2025)
- [Statistically Reliable LLM-Based Ranking Evaluation via Prediction-Powered Inference](https://mlsanity.com/paper/2606.05308/) (2026)
- [Ranking Policy Learning via Marketplace Expected Value Estimation From Observational Data](https://mlsanity.com/paper/2410.04568/) (2024)
- [RewardRank: Optimizing True Learning-to-Rank Utility](https://mlsanity.com/paper/2508.14180/) (2025)
- [Exposure-Based Reinforcement Learning to Rank](https://mlsanity.com/paper/2607.18689/) (2026)
- [Sequential Multimodal Evidence Optimization for Product Media Ranking in E-Commerce](https://mlsanity.com/paper/2608.15662/) (2026)
- [Recommendation Ranking Off-Policy Evaluation under Ranking-Dependent Examination via Examination-Relevance Decomposition](https://mlsanity.com/paper/2609.35034/) (2026)
- [Bias Robustness of Genetic Multi-Criteria Sorting versus Learned Rankers under Proxy Skew and Label Contamination](https://mlsanity.com/paper/2610.14015/) (2026)

## Abstract (arXiv)

Clicks on rankings suffer from position-bias: generally items on lower ranks are less likely to be examined - and thus clicked - by users, in spite of their actual preferences between items. The prevalent approach to unbiased click-based learning-to-rank (LTR) is based on counterfactual inverse-propensity-scoring (IPS) estimation. In contrast with general reinforcement learning, counterfactual doubly-robust (DR) estimation has not been applied to click-based LTR in previous literature. In this paper, we introduce a novel DR estimator that is the first DR approach specifically designed for position-bias. The difficulty with position-bias is that the treatment - user examination - is not directly observable in click data. As a solution, our estimator uses the expected treatment per rank, instead of the actual treatment that existing DR estimators use. Our novel DR estimator has more robust unbiasedness conditions than the existing IPS approach, and in addition, provides enormous decreases in variance: our experimental results indicate it requires several orders of magnitude fewer datapoints to converge at optimal performance. For the unbiased LTR field, our DR estimator contributes both increases in state-of-the-art performance and the most robust theoretical guarantees of all known LTR estimators.