# A Control Function Framework for Mitigating Position Bias in Learning to Rank Systems

arXiv: https://arxiv.org/abs/2506.06989 · HTML: https://mlsanity.com/paper/2506.06989/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 66 references that are in the map.
- First posted on arXiv 8 Jun 2025.

## Builds on (most cited first, 17 of 17)

- [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 Learning to Rank with Unbiased Propensity Estimation](https://mlsanity.com/paper/1804.05938/) (2018)
- [Optimal Regret Analysis of Thompson Sampling in Stochastic Multi-armed Bandit Problem with Multiple Plays](https://mlsanity.com/paper/1506.00779/) (2015)
- [Correcting for Selection Bias in Learning-to-rank Systems](https://mlsanity.com/paper/2001.11358/) (2020)
- [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)
- [Doubly-Robust Estimation for Correcting Position-Bias in Click Feedback for Unbiased Learning to Rank](https://mlsanity.com/paper/2203.17118/) (2022)
- [Distributionally Robust Graph-based Recommendation System](https://mlsanity.com/paper/2402.12994/) (2024)
- [Intervention Harvesting for Context-Dependent Examination-Bias Estimation](https://mlsanity.com/paper/1811.01802/) (2018)
- [A Large Scale Search Dataset for Unbiased Learning to Rank](https://mlsanity.com/paper/2207.03051/) (2022)
- [Graph Representation Learning via Causal Diffusion for Out-of-Distribution Recommendation](https://mlsanity.com/paper/2408.00490/) (2024)
- [Unbiased Learning to Rank Meets Reality: Lessons from Baidu's Large-Scale Search Dataset](https://mlsanity.com/paper/2404.02543/) (2024)
- [Towards Disentangling Relevance and Bias in Unbiased Learning to Rank](https://mlsanity.com/paper/2212.13937/) (2022)
- [Model-based Unbiased Learning to Rank](https://mlsanity.com/paper/2207.11785/) (2022)
- [Counterfactual Learning to Rank using Heterogeneous Treatment Effect Estimation](https://mlsanity.com/paper/2007.09798/) (2020)
- [Approximated Doubly Robust Search Relevance Estimation](https://mlsanity.com/paper/2208.07671/) (2022)

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

- [MetaSynth: Multi-Agent Metadata Generation from Implicit Feedback in Black-Box Systems](https://mlsanity.com/paper/2510.01523/) (2025)

## Abstract (arXiv)

Learning-to-rank (LTR) systems commonly depend on implicit feedback, such as user clicks, because it is easy to collect and can serve as a valuable signal of user preferences. However, directly optimizing ranking models using implicit feedback data often yields suboptimal performance because such data is inherently skewed by systematic biases. Among these biases, position bias is particularly pervasive: items ranked higher tend to receive disproportionately more interactions, regardless of their actual relevance. To address this, we introduce a novel two-stage framework based on control functions. In the first stage, we utilize exogenous variation from the residuals of the ranking process, which are then incorporated into a second stage click model to account for position-dependent distortions. In contrast to existing methods, our approach avoids explicit propensity estimation, supports nonlinear ranking models, and can be flexibly incorporated into any state-of-the-art ranking algorithm for position bias correction. We also propose a debiasing strategy for validation clicks that enables reliable hyperparameter tuning in the absence of unbiased validation data. Empirical results show that our method outperforms state-of-the-art position bias correction methods on both benchmark and real-world industrial datasets.