Learning Optimal Stable Matches in Decentralized Markets with Unknown Preferences

2024-09-07

arXiv.org

AI Summary

This paper addresses decentralized bilateral matching markets without central coordination and with unknown agent preferences. Method: We propose the first fully decoupled, communication-free online learning algorithm wherein proposers autonomously learn their preferences through repeated interactions—requiring no prior information or global knowledge. The approach integrates stable matching theory, stochastic approximation, and game-theoretic modeling. Contribution/Results: We rigorously prove that, regardless of market structure, the algorithm converges almost surely to the proposer-optimal stable matching—a solution that simultaneously maximizes social welfare. Crucially, our framework eliminates reliance on centralized information, explicit coordination mechanisms, or exogenous signaling; it is the first to achieve purely decentralized, adaptive, and theoretically guaranteed optimal stable matching learning.

Technology Category

• Search and Optimization: Learning to Search
• Multiagent Systems: Mechanism Design
• Machine Learning: Learning Preferences or Rankings

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs

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.

Problem

• Distributed Market
• Matching Algorithm
• Decentralized Learning

Innovation

• Decentralized Algorithm
• Information-constrained Matching
• Learning Process