Putting Gale & Shapley to Work: Guaranteeing Stability Through Learning
Research Poster Arts & Humanities 2025 Graduate ExhibitionPresentation by Duohan Zhang
Exhibition Number 10
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.
Importance
The game-theoretical properties such as stability in two-sided matching problems are critical indicators of success and sustenance of matching markets; without stability agents may ‘scramble’ to participate in secondary markets even when all preferences are known. We demonstrated key techniques in learning preferences that rely on the structure of stable solutions. In particular, exploiting the known preferences of arms in the arm-proposing variant of DA and eliminating arms early on, provably reduces the sample complexity of finding stable matchings while experimentally having little impact on optimality(measured by regret). Findings of this paper can have substantial impact in designing new labor markets, school admissions, or healthcare where decisions must be made as preferences are revealed.