# Fast solution to the fair ranking problem using the Sinkhorn algorithm

arXiv: https://arxiv.org/abs/2406.10262 · HTML: https://mlsanity.com/paper/2406.10262/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 10 references that are in the map.
- First posted on arXiv 11 Jun 2024.

## Builds on (most cited first, 8 of 8)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Sinkhorn Distances: Lightspeed Computation of Optimal Transportation Distances](https://mlsanity.com/paper/1306.0895/) (2013)
- [Fairness of Exposure in Rankings](https://mlsanity.com/paper/1802.07281/) (2018)
- [Equity of Attention: Amortizing Individual Fairness in Rankings](https://mlsanity.com/paper/1805.01788/) (2018)
- [FairRec: Two-Sided Fairness for Personalized Recommendations in Two-Sided Platforms](https://mlsanity.com/paper/2002.10764/) (2020)
- [Fairness in Rankings and Recommendations: An Overview](https://mlsanity.com/paper/2104.05994/) (2021)
- [Fair Ranking as Fair Division: Impact-Based Individual Fairness in Ranking](https://mlsanity.com/paper/2206.07247/) (2022)
- [Scalable and Provably Fair Exposure Control for Large-Scale Recommender Systems](https://mlsanity.com/paper/2402.14369/) (2024)

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

- [Subset Selection for Stratified Sampling in Online Controlled Experiments](https://mlsanity.com/paper/2509.15576/) (2025)

## Abstract (arXiv)

In two-sided marketplaces such as online flea markets, recommender systems for providing consumers with personalized item rankings play a key role in promoting transactions between providers and consumers. Meanwhile, two-sided marketplaces face the problem of balancing consumer satisfaction and fairness among items to stimulate activity of item providers. Saito and Joachims (2022) devised an impact-based fair ranking method for maximizing the Nash social welfare based on fair division; however, this method, which requires solving a large-scale constrained nonlinear optimization problem, is very difficult to apply to practical-scale recommender systems. We thus propose a fast solution to the impact-based fair ranking problem. We first transform the fair ranking problem into an unconstrained optimization problem and then design a gradient ascent method that repeatedly executes the Sinkhorn algorithm. Experimental results demonstrate that our algorithm provides fair rankings of high quality and is about 1000 times faster than application of commercial optimization software.