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.

本研究针对双边匹配市场中的稳定性问题，提出了一种新的算法，通过利用稳定解的结构来提高找到稳定匹配的可能性。研究着重分析了达到高概率稳定匹配所需的样本复杂度，并通过实证结果揭示了所提算法在稳定性与最优性之间的有趣权衡，进而丰富了理论理解。

将盖尔和沙普利应用于实践：通过学习保证稳定性