用纳什公平性优化匹配平台推荐，兼顾公平与高匹配率
Balancing Fairness and High Match Rates in Reciprocal Recommender Systems: A Nash Social Welfare Approach
- 引入纳什社会福利方法，交替优化两个目标函数实现近似公平推荐
- 相比传统方法，新方案使推荐机会分配更公平，匹配率仍保持高位
- 适合关注推荐系统公平性与效率平衡的研究者和平台设计者
匹配平台如在线约会和职位推荐日益普及。为确保平台成功，需设计既能提升总匹配数又避免用户间不公平的互惠推荐系统（RRS）。本文从公平分配视角定义用户被推荐的机会，并建立该机会分配的免嫉妒公平性概念。首先引入社会福利（SW）方法，近似最大化匹配数，但导致显著不公平，揭示公平与匹配率之间的权衡。为此，提出纳什社会福利（NSW）方法，通过交替优化两个NSW函数，实现近乎免嫉妒的推荐。进一步将SW与NSW推广至α-SW方法，以灵活平衡公平与高匹配率。此外，基于Sinkhorn算法开发了高效的近似算法。在合成数据集及两个真实世界数据集上的大量实验验证了方法的有效性。
原文摘要 · Abstract (English)
Matching platforms, such as online dating services and job recommendations, have become increasingly prevalent. For the success of these platforms, it is crucial to design reciprocal recommender systems (RRSs) that not only increase the total number of matches but also avoid creating unfairness among users. In this paper, we investigate the fairness of RRSs on matching platforms. From the perspective of fair division, we define the users' opportunities to be recommended and establish the fairness concept of envy-freeness in the allocation of these opportunities. We first introduce the Social Welfare (SW) method, which approximately maximizes the number of matches, and show that it leads to significant unfairness in recommendation opportunities, illustrating the trade-off between fairness and match rates. To address this challenge, we propose the Nash Social Welfare (NSW) method, which alternately optimizes two NSW functions and achieves nearly envy-free recommendations. We further generalize the SW and NSW method to the $α$-SW method, which balances the trade-off between fairness and high match rates. Additionally, we develop a computationally efficient approximation algorithm for the SW/NSW/$α$-SW methods based on the Sinkhorn algorithm. Through extensive experiments on both synthetic datasets and two real-world datasets, we demonstrate the practical effectiveness of our approach.
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