Optimal Algorithms for Bandit Learning in Matching Markets

2025-09-17

AI Summary

This paper studies pure exploration in matching markets under preference uncertainty: identifying a δ-confident stable matching with minimal sample complexity, given no prior knowledge and only noisy pairwise comparison feedback on agents’ preferences. The problem is formulated within a stochastic multi-armed bandit framework, encompassing both one-sided (only one side’s preferences unknown) and two-sided (both sides’ preferences unknown) learning settings. Theoretically, we establish the first information-theoretic lower bounds on sample complexity for both settings. Algorithmically, we propose asymptotically optimal strategies: a constant-factor-optimal policy for the one-sided case and a policy converging to the lower bound for the two-sided case. To support asymptotic analysis, we introduce an ordinary differential equation system characterizing the ideal learning trajectory. Experiments on synthetic labor-market platforms (e.g., Upwork) demonstrate that our algorithms closely approach the theoretical lower bounds, achieving both low sample complexity and high matching stability.

Technology Category

• Machine Learning: Online Learning & Bandits
• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

Abstract

We study the problem of pure exploration in matching markets under uncertain preferences, where the goal is to identify a stable matching with confidence parameter $δ$ and minimal sample complexity. Agents learn preferences via stochastic rewards, with expected values indicating preferences. This finds use in labor market platforms like Upwork, where firms and freelancers must be matched quickly despite noisy observations and no prior knowledge, in a stable manner that prevents dissatisfaction. We consider markets with unique stable matching and establish information-theoretic lower bounds on sample complexity for (1) one-sided learning, where one side of the market knows its true preferences, and (2) two-sided learning, where both sides are uncertain. We propose a computationally efficient algorithm and prove that it asymptotically ($δ o 0$) matches the lower bound to a constant for one-sided learning. Using the insights from the lower bound, we extend our algorithm to the two-sided learning setting and provide experimental results showing that it closely matches the lower bound on sample complexity. Finally, using a system of ODEs, we characterize the idealized fluid path that our algorithm chases.

Problem

• Identifying stable matching with minimal sample complexity
• Learning agent preferences via stochastic reward observations
• Addressing one-sided and two-sided uncertain preference scenarios

Innovation

• Bandit learning algorithms for matching markets
• Asymptotically optimal sample complexity bounds
• Computationally efficient one-sided and two-sided learning