Match Made with Matrix Completion: Efficient Learning under Matching Interference

2026-01-11

AI Summary

This study addresses the challenge of learning high-quality matchings in two-sided markets where observed matching outcomes are high-dimensional and subject to dependence induced by matching or budget constraints—referred to as matching interference. Leveraging the low-rank structure of the underlying utility matrix, the authors propose a nuclear-norm-regularized matrix completion approach and provide the first theoretical guarantee of its effectiveness under matching interference. They introduce a “doubly debiased” estimator that achieves near-optimal entrywise error bounds and Frobenius norm guarantees. The method is further extended to an online matching setting with dependent sampling, yielding improved regret bounds. Empirical evaluations on both synthetic and real-world labor market data demonstrate the practical efficacy of the proposed approach.

Technology Category

• Machine Learning: Matrix & Tensor Methods
• Game Theory and Economic Paradigms: Mechanism Design
• Multiagent Systems: Mechanism Design

Application Category

• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems
• 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

Matching markets face increasing needs to learn the matching qualities between demand and supply for effective design of matching policies. In practice, the matching rewards are high-dimensional due to the growing diversity of participants. We leverage a natural low-rank matrix structure of the matching rewards in these two-sided markets, and propose to utilize matrix completion to accelerate reward learning with limited offline data. A unique property for matrix completion in this setting is that the entries of the reward matrix are observed with matching interference -- i.e., the entries are not observed independently but dependently due to matching or budget constraints. Such matching dependence renders unique technical challenges, such as sub-optimality or inapplicability of the existing analytical tools in the matrix completion literature, since they typically rely on sample independence. In this paper, we first show that standard nuclear norm regularization remains theoretically effective under matching interference. We provide a near-optimal Frobenius norm guarantee in this setting, coupled with a new analytical technique. Next, to guide certain matching decisions, we develop a novel ``double-enhanced''estimator, based off the nuclear norm estimator, with a near-optimal entry-wise guarantee. Our double-enhancement procedure can apply to broader sampling schemes even with dependence, which may be of independent interest. Additionally, we extend our approach to online learning settings with matching constraints such as optimal matching and stable matching, and present improved regret bounds in matrix dimensions. Finally, we demonstrate the practical value of our methods using both synthetic data and real data of labor markets.

Problem

• matching markets
• matrix completion
• matching interference
• reward learning
• dependent observations

Innovation

• matrix completion
• matching interference
• nuclear norm regularization
• double-enhanced estimator
• online matching