# Learning to Rank with Top-K Fairness

arXiv: https://arxiv.org/abs/2509.18067 · HTML: https://mlsanity.com/paper/2509.18067/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 25 of its 47 references that are in the map.
- First posted on arXiv 22 Sep 2025.

## Builds on (most cited first, 25 of 25)

- [Equality of Opportunity in Supervised Learning](https://mlsanity.com/paper/1610.02413/) (2016)
- [Neural Collaborative Filtering](https://mlsanity.com/paper/1708.05031/) (2017)
- [Fairness Beyond Disparate Treatment & Disparate Impact: Learning Classification without Disparate Mistreatment](https://mlsanity.com/paper/1610.08452/) (2016)
- [Approximation Methods for Bilevel Programming](https://mlsanity.com/paper/1802.02246/) (2018)
- [Fairness of Exposure in Rankings](https://mlsanity.com/paper/1802.07281/) (2018)
- [Fairness in Recommendation Ranking through Pairwise Comparisons](https://mlsanity.com/paper/1903.00780/) (2019)
- [Equity of Attention: Amortizing Individual Fairness in Rankings](https://mlsanity.com/paper/1805.01788/) (2018)
- [FA*IR: A Fair Top-k Ranking Algorithm](https://mlsanity.com/paper/1706.06368/) (2017)
- [Measuring Fairness in Ranked Outputs](https://mlsanity.com/paper/1610.08559/) (2016)
- [Ranking with Fairness Constraints](https://mlsanity.com/paper/1704.06840/) (2017)
- [Policy Learning for Fairness in Ranking](https://mlsanity.com/paper/1902.04056/) (2019)
- [iFair: Learning Individually Fair Data Representations for Algorithmic Decision Making](https://mlsanity.com/paper/1806.01059/) (2018)
- [Pairwise Fairness for Ranking and Regression](https://mlsanity.com/paper/1906.05330/) (2019)
- [Designing Fair Ranking Schemes](https://mlsanity.com/paper/1712.09752/) (2017)
- [Reducing Disparate Exposure in Ranking: A Learning To Rank Approach](https://mlsanity.com/paper/1805.08716/) (2018)
- [Large-scale Stochastic Optimization of NDCG Surrogates for Deep Learning with Provable Convergence](https://mlsanity.com/paper/2202.12183/) (2022)
- [Quantifying Search Bias: Investigating Sources of Bias for Political Searches in Social Media](https://mlsanity.com/paper/1704.01347/) (2017)
- [End-to-end Learning for Fair Ranking Systems](https://mlsanity.com/paper/2111.10723/) (2021)
- [Fair Ranking with Noisy Protected Attributes](https://mlsanity.com/paper/2211.17067/) (2022)
- [Understanding Fairness Surrogate Functions in Algorithmic Fairness](https://mlsanity.com/paper/2310.11211/) (2023)
- [Fairness for Robust Learning to Rank](https://mlsanity.com/paper/2112.06288/) (2021)
- [Fair Rank Aggregation](https://mlsanity.com/paper/2308.10499/) (2023)
- [FAIR: Fairness-Aware Information Retrieval Evaluation](https://mlsanity.com/paper/2106.08527/) (2021)
- [Vertical Allocation-based Fair Exposure Amortizing in Ranking](https://mlsanity.com/paper/2204.03046/) (2022)
- [The Impact of Group Membership Bias on the Quality and Fairness of Exposure in Ranking](https://mlsanity.com/paper/2308.02887/) (2023)

## Abstract (arXiv)

Fairness in ranking models is crucial, as disparities in exposure can disproportionately affect protected groups. Most fairness-aware ranking systems focus on ensuring comparable average exposure for groups across the entire ranked list, which may not fully address real-world concerns. For example, when a ranking model is used for allocating resources among candidates or disaster hotspots, decision-makers often prioritize only the top-K ranked items, while the ranking beyond top-K becomes less relevant. In this paper, we propose a list-wise learning-to-rank framework that addresses the issues of inequalities in top-K rankings at training time. Specifically, we propose a top-K exposure disparity measure that extends the classic exposure disparity metric in a ranked list. We then learn a ranker to balance relevance and fairness in top-K rankings. Since direct top-K selection is computationally expensive for a large number of items, we transform the non-differentiable selection process into a differentiable objective function and develop efficient stochastic optimization algorithms to achieve both high accuracy and sufficient fairness. Extensive experiments demonstrate that our method outperforms existing methods.