Stable Matching with Predictions: Robustness and Efficiency under Pruned Preferences

TL;DR

This paper investigates stable matching with truncated preferences based on predictions, demonstrating that the classic deferred-acceptance algorithm remains robust and efficient, reducing preference list lengths and proposals in large markets.

Contribution

It introduces algorithms for stable matching with truncated preferences using predictions, showing robustness and efficiency improvements both theoretically and empirically.

Findings

Predictions enable significant reduction in preference list lengths.

The deferred-acceptance algorithm remains robust under preference truncation.

Empirical results confirm efficiency gains in large matching markets.

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.