Fast solution to the fair ranking problem using the Sinkhorn algorithm

TL;DR

This paper introduces a fast, scalable algorithm for fair ranking in two-sided marketplaces, transforming the problem into an unconstrained optimization and using Sinkhorn-based gradient ascent, achieving significant speed improvements.

Contribution

The authors develop a novel, efficient algorithm for impact-based fair ranking by combining problem transformation and Sinkhorn algorithm, enabling practical large-scale application.

Findings

Algorithm is approximately 1000 times faster than commercial solvers.

Produces high-quality fair rankings in large-scale settings.

Effective in promoting fairness without sacrificing ranking quality.

Abstract

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.