Learning Optimal Stable Matches in Decentralized Markets with Unknown Preferences

TL;DR

This paper introduces a decentralized, communication-free online learning algorithm that enables agents in a two-sided matching market to independently learn preferences and converge to the optimal stable match, without prior knowledge or centralized coordination.

Contribution

It presents the first fully decoupled, limited-information algorithm that guarantees probabilistic convergence to the welfare-maximizing stable match in decentralized markets.

Findings

Guarantees probabilistic convergence to the proposer-optimal stable match.

Operates without prior preference knowledge or communication.

Applicable to arbitrary market structures.

Abstract

Matching algorithms have demonstrated great success in several practical applications, but they often require centralized coordination and plentiful information. In many modern online marketplaces, agents must independently seek out and match with another using little to no information. For these kinds of settings, can we design decentralized, limited-information matching algorithms that preserve the desirable properties of standard centralized techniques? In this work, we constructively answer this question in the affirmative. We model a two-sided matching market as a game consisting of two disjoint sets of agents, referred to as proposers and acceptors, each of whom seeks to match with their most preferable partner on the opposite side of the market. However, each proposer has no knowledge of their own preferences, so they must learn their preferences while forming matches in the market. We present a simple online learning rule that guarantees a strong notion of probabilistic convergence to the welfare-maximizing equilibrium of the game, referred to as the proposer-optimal stable match. To the best of our knowledge, this represents the first completely decoupled, communication-free algorithm that guarantees probabilistic convergence to an optimal stable match, irrespective of the structure of the matching market.