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Fast solution to the fair ranking problem using the Sinkhorn algorithm

Yuki Uehara, Shunnosuke Ikeda, Naoki Nishimura, Koya Ohashi, Yilin Li, Jie Yang, Deddy Jobson, Xingxia Zha, Takeshi Matsumoto, Noriyoshi Sukegawa, Yuichi Takano

TL;DR

This work first transforms the fair ranking problem into an unconstrained optimization problem and then design a gradient ascent method that repeatedly executes the Sinkhorn algorithm, which provides fair rankings of high quality and is about 1000 times faster than application of commercial optimization software.

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.

Fast solution to the fair ranking problem using the Sinkhorn algorithm

TL;DR

This work first transforms the fair ranking problem into an unconstrained optimization problem and then design a gradient ascent method that repeatedly executes the Sinkhorn algorithm, which provides fair rankings of high quality and is about 1000 times faster than application of commercial optimization software.

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.
Paper Structure (6 sections, 1 theorem, 3 equations, 3 figures, 1 algorithm)

This paper contains 6 sections, 1 theorem, 3 equations, 3 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Impact-based fair ranking problem
  3. Gradient ascent method using the Sinkhorn algorithm
  4. Experiments
  5. Experimental setup
  6. Results and conclusion

Key Result

theorem thmcountertheorem

For any $\bm{X}_u$ satisfying Eqs. eq:dsm1--eq:dsm4, there exists $\bm{C}_u$ such that $\bm{X}_u = \bm{X}_u^{\star}(\bm{C}_u)$.

Figures (3)

  • Figure 1: Evaluation metrics for the synthetic dataset ($|U|=1000$, $|I|=500$, $m=11$)
  • Figure 2: Evaluation metrics for the Delicious dataset ($|U|=1014$, $|I|=100$, $m=11$)
  • Figure 3: Computation times for the synthetic dataset ($|U|=250$, $|I|=250$, $m=11$)

Theorems & Definitions (2)

  • theorem thmcountertheorem
  • proof