Probably Correct Optimal Stable Matching under Two-Sided Uncertainty

2026-07-06

AI Summary

This work addresses the problem of efficiently identifying the optimal stable matching with high probability in a two-sided market where preferences on both sides are initially unknown. Within a pure exploration framework, the algorithm sequentially matches agents and receives noisy reward feedback from both sides, gradually learning partial preference information. The paper introduces the novel concept of a “universally stable matching” to handle preference uncertainty and proposes an elimination-based algorithm that integrates a semi-bandit feedback model with partial preference inference. Theoretical analysis shows that the proposed algorithm, under the pure exploration setting, satisfies a rigorous stopping criterion and correctly identifies the optimal stable matching with high probability. Furthermore, in the regret minimization setting, it achieves the first theoretical guarantee that does not depend on the minimum reward gap (Δ_min).

Abstract

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 $Δ_{\min}$.

Problem

• stable matching
• two-sided uncertainty
• pure exploration
• partial preferences
• sequential learning

Innovation

• two-sided uncertainty
• partial preference
• pervasive stable matching
• pure exploration
• regret minimization