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Stable Matching with Predictions: Robustness and Efficiency under Pruned Preferences

Samuel McCauley, Benjamin Moseley, Helia Niaparast, Shikha Singh

TL;DR

The paper studies stable matching under pruned preferences guided by predictions. It introduces two learning-augmented truncation schemes, window-truncated DA (WDA) and prefix-truncated DA (PDA), and proves safety and efficiency guarantees for WDA when a stable solution lies in the pruned window, while PDA provides robustness to mispredictions by adaptively extending lists. A lower bound shows that without a promise that a stable matching exists within the pruned instance, improved efficiency cannot be guaranteed, underscoring fundamental limits. The authors complement theory with empirical evaluation across Mallows, dating, and tiered markets, showing substantial reductions in proposal counts and input sizes, and practical viability for large-scale matching like NRMP. The work bridges market design and algorithms-with-predictions, offering a principled path to scalable, stable matching in data-constrained settings.

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.

Stable Matching with Predictions: Robustness and Efficiency under Pruned Preferences

TL;DR

The paper studies stable matching under pruned preferences guided by predictions. It introduces two learning-augmented truncation schemes, window-truncated DA (WDA) and prefix-truncated DA (PDA), and proves safety and efficiency guarantees for WDA when a stable solution lies in the pruned window, while PDA provides robustness to mispredictions by adaptively extending lists. A lower bound shows that without a promise that a stable matching exists within the pruned instance, improved efficiency cannot be guaranteed, underscoring fundamental limits. The authors complement theory with empirical evaluation across Mallows, dating, and tiered markets, showing substantial reductions in proposal counts and input sizes, and practical viability for large-scale matching like NRMP. The work bridges market design and algorithms-with-predictions, offering a principled path to scalable, stable matching in data-constrained settings.

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.
Paper Structure (35 sections, 14 theorems, 9 equations, 3 figures)

This paper contains 35 sections, 14 theorems, 9 equations, 3 figures.

Table of Contents

  1. Introduction
  2. Our Model: Algorithms with Predictions
  3. Stable Matching with Predictions
  4. Prediction model and truncation algorithms.
  5. Our Contributions
  6. Window-truncated DA.
  7. Prefix-truncated DA.
  8. Lower bound on efficiency if prediction-based truncation eliminates all stable matchings.
  9. Empirical evaluation.
  10. Recovering intermediate stable matchings.
  11. Related Work
  12. Stable matchings.
  13. Algorithms with predictions.
  14. Preliminaries
  15. Window-Truncated DA Algorithm
  16. ...and 20 more sections

Key Result

Theorem 2.1

For any instance of the stable matching problem, the DA algorithm terminates in $O(n^2)$ time, and the matching produced at termination is stable.

Figures (3)

  • Figure 1: A counterexample showing that truncating preference lists of proposers can fail.
  • Figure 2: Proposal counts for classic DA, WDA, and PDA across the three market models. The green numbers show the percentage of instances in which WDA finds a stable matching.
  • Figure 3: Instance size for WDA and PDA across the three market models.

Theorems & Definitions (25)

  • Theorem 2.1
  • Theorem 2.2
  • Lemma 3.1
  • proof
  • Lemma 3.2
  • proof
  • Lemma 3.3
  • proof
  • Theorem 3.4
  • proof
  • ...and 15 more