Probably Correct Optimal Stable Matching for Two-Sided Markets Under Uncertainty

2025-01-06

AI Summary

This paper addresses bilateral matching markets where agents’ preferences are unknown and feedback is noisy, focusing on enabling left-side agents (e.g., buyers) to efficiently learn and achieve their optimal stable matching. Method: It is the first to formulate stable matching as a pure-exploration multi-armed bandit problem with noisy preference feedback; introduces the novel learning objective of “possibly correct optimal stable matching”; and proposes a confidence-aware active learning algorithm integrating stable matching theory, bandit learning, confidence interval estimation, and sequential decision-making. Contribution/Results: The algorithm enjoys theoretical guarantees on sample complexity, with an upper bound derived under mild assumptions. Empirical evaluation on synthetic data demonstrates that it significantly outperforms baselines—achieving rapid, high-probability convergence to the left-optimal stable matching while substantially reducing exploration cost under preference uncertainty.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Constraint Satisfaction and Optimization: Constraint Learning and Acquisition

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 consider a learning problem for the stable marriage model under unknown preferences for the left side of the market. We focus on the centralized case, where at each time step, an online platform matches the agents, and obtains a noisy evaluation reflecting their preferences. Our aim is to quickly identify the stable matching that is left-side optimal, rendering this a pure exploration problem with bandit feedback. We specifically aim to find Probably Correct Optimal Stable Matchings and present several bandit algorithms to do so. Our findings provide a foundational understanding of how to efficiently gather and utilize preference information to identify the optimal stable matching in two-sided markets under uncertainty. An experimental analysis on synthetic data complements theoretical results on sample complexities for the proposed methods.

Problem

• Stable Matching
• Information Uncertainty
• Online Platform

Innovation

• Stable Matching
• Error-prone Preference
• Efficient Strategies