Probably Correct Optimal Stable Matching under Two-Sided Uncertainty
For centralized matching platforms (e.g., labor markets, school choice), this work provides the first algorithm for optimal stable matching under two-sided uncertainty with provable guarantees.
This paper addresses the problem of efficiently identifying the optimal stable matching in two-sided markets under unknown preferences with noisy feedback. The proposed elimination-based algorithms achieve high-probability correctness with refined sample complexity, and extend to regret minimization with bounds independent of the minimum reward gap.
We study a sequential learning problem for stable matchings in two-sided markets where preferences on both sides are initially unknown. We focus on a centralized setting where an algorithm matches agents at each time step and receives noisy rewards that reflect the preferences of the matched agents, following a semi-bandit feedback structure. We adopt a pure exploration perspective, aiming to efficiently identify the optimal stable matching with high probability. Our work extends prior results by handling \emph{two-sided uncertainty} and by exploiting \emph{partial preference} information. A central ingredient is the notion of \textbf{pervasive stable matching}, which enables the identification of optimal stable matchings under partial preferences. We propose elimination-based algorithms whose stopping criteria exploit the structure of the learned partial preferences, and provide a refined sample-complexity analysis. Beyond pure exploration, we extend our approach to regret minimization and establish regret bounds with respect to the \emph{optimal} stable matching that avoid dependence on the minimum reward gap $Δ_{\min}$.