Bandit Learning in Matching Markets: Utilitarian and Rawlsian Perspectives

TL;DR

This paper explores learning algorithms for two-sided matching markets using bandit models, aiming to optimize welfare metrics like utilitarian and Rawlsian while ensuring market stability, with theoretical analysis and simulations.

Contribution

It introduces algorithms based on epoch Explore-Then-Commit for welfare optimization in matching markets with unknown preferences, analyzing their regret bounds.

Findings

Algorithms achieve sublinear regret bounds.

Welfare metrics improve with more learning epochs.

Market stability is maintained during learning.

Abstract

Two-sided matching markets have demonstrated significant impact in many real-world applications, including school choice, medical residency placement, electric vehicle charging, ride sharing, and recommender systems. However, traditional models often assume that preferences are known, which is not always the case in modern markets, where preferences are unknown and must be learned. For example, a company may not know its preference over all job applicants a priori in online markets. Recent research has modeled matching markets as multi-armed bandit (MAB) problem and primarily focused on optimizing matching for one side of the market, while often resulting in a pessimal solution for the other side. In this paper, we adopt a welfarist approach for both sides of the market, focusing on two metrics: (1) Utilitarian welfare and (2) Rawlsian welfare, while maintaining market stability. For these metrics, we propose algorithms based on epoch Explore-Then-Commit (ETC) and analyze their regret bounds. Finally, we conduct simulated experiments to evaluate both welfare and market stability.