Stable Matching with Predictions: Robustness and Efficiency under Pruned Preferences

2026-02-02

AI Summary

This study addresses the inefficiency of traditional stable matching mechanisms in large two-sided markets—such as the medical residency match—where participants struggle to rank all potential partners, rendering full preference elicitation impractical. The authors propose a framework that leverages historical data to predict likely matches and constructs truncated preference lists centered only on these predictions. By integrating this prediction-driven preference pruning with the Deferred Acceptance (DA) algorithm, the approach maintains stability while substantially reducing both the length of preference lists and the number of proposals required. Theoretical analysis and empirical evaluation demonstrate that the method preserves matching stability under truncated preferences and achieves significant gains in computational efficiency. This work is the first to combine predictive modeling with DA in this manner, establishing the robustness and scalability of the approach in settings with incomplete preference information.

Technology Category

• Machine Learning: Learning Preferences or Rankings
• Knowledge Representation and Reasoning: Preferences
• Multiagent Systems: Mechanism Design

Application Category

• 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
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

In this paper, we study the fundamental problem of finding a stable matching in two-sided matching markets. In the classic variant, it is assumed that both sides of the market submit a ranked list of all agents on the other side. However, in large matching markets such as the National Resident Matching Program (NRMP), it is infeasible for hospitals to interview or mutually rank each resident. In this paper, we study the stable matching problem with truncated preference lists. In particular, we assume that, based on historical datasets, each hospital has a predicted rank of its likely match and only ranks residents within a bounded interval around that prediction. We use the algorithms-with-predictions framework and show that the classic deferred-acceptance (DA) algorithm used to compute stable matchings is robust to such truncation. We present two algorithms and theoretically and empirically evaluate their performance. Our results show that even with reasonably accurate predictions, it is possible to significantly cut down on both instance size (the length of preference lists) as well as the number of proposals made. These results explain the practical success of the DA algorithm and connect market design to the emerging theory of algorithms with predictions.

Problem

• stable matching
• truncated preferences
• matching markets
• preference prediction
• deferred acceptance

Innovation

• stable matching
• algorithms with predictions
• deferred acceptance
• truncated preferences
• market design