Putting Gale & Shapley to Work: Guaranteeing Stability Through Learning

TL;DR

This paper develops algorithms for learning preferences in two-sided matching markets to ensure stable matchings, providing theoretical bounds and empirical insights into the tradeoffs between stability and optimality.

Contribution

It introduces the first study on the sample complexity of achieving stable matchings through learning in market settings.

Findings

Theoretical bounds on sample complexity for stable matchings.

Algorithms that improve the likelihood of stable solutions.

Empirical evidence of tradeoffs between stability and optimality.

Abstract

Two-sided matching markets describe a large class of problems wherein participants from one side of the market must be matched to those from the other side according to their preferences. In many real-world applications (e.g. content matching or online labor markets), the knowledge about preferences may not be readily available and must be learned, i.e., one side of the market (aka agents) may not know their preferences over the other side (aka arms). Recent research on online settings has focused primarily on welfare optimization aspects (i.e. minimizing the overall regret) while paying little attention to the game-theoretic properties such as the stability of the final matching. In this paper, we exploit the structure of stable solutions to devise algorithms that improve the likelihood of finding stable solutions. We initiate the study of the sample complexity of finding a stable matching, and provide theoretical bounds on the number of samples needed to reach a stable matching with high probability. Finally, our empirical results demonstrate intriguing tradeoffs between stability and optimality of the proposed algorithms, further complementing our theoretical findings.