Who With Whom? Learning Optimal Matching Policies

2025-07-17

AI Summary

This paper addresses the problem of learning socially optimal bilateral matching policies—such as jobseeker–employment counselor assignment—based on observable features of both sides. Methodologically, it formulates optimal matching as an empirical optimal transport problem with estimated matching costs and introduces a novel entropy-regularized empirical welfare maximization framework that jointly estimates costs via nonparametric regression and solves for the matching policy using statistical learning theory. Theoretically, the approach provides provable welfare regret bounds and convergence guarantees. Empirically, calibrated simulations using French administrative data demonstrate that the proposed method significantly improves welfare outcomes in employment assistance programs, validating its effectiveness, practical relevance, and scalability in real-world economic settings.

Technology Category

• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning
• Planning, Routing, and Scheduling: Learning for Planning and Scheduling

Application Category

• Economics, Online Markets and Human Computation: Social networks and social learning
• 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

There are many economic contexts where the productivity and welfare performance of institutions and policies depend on who matches with whom. Examples include caseworkers and job seekers in job search assistance programs, medical doctors and patients, teachers and students, attorneys and defendants, and tax auditors and taxpayers, among others. Although reallocating individuals through a change in matching policy can be less costly than training personnel or introducing a new program, methods for learning optimal matching policies and their statistical performance are less studied than methods for other policy interventions. This paper develops a method to learn welfare optimal matching policies for two-sided matching problems in which a planner matches individuals based on the rich set of observable characteristics of the two sides. We formulate the learning problem as an empirical optimal transport problem with a match cost function estimated from training data, and propose estimating an optimal matching policy by maximizing the entropy regularized empirical welfare criterion. We derive a welfare regret bound for the estimated policy and characterize its convergence. We apply our proposal to the problem of matching caseworkers and job seekers in a job search assistance program, and assess its welfare performance in a simulation study calibrated with French administrative data.

Problem

• Learning optimal matching policies for economic productivity
• Developing methods for two-sided matching with observable characteristics
• Evaluating welfare performance in job seeker-caseworker matching

Innovation

• Estimates optimal matching via empirical transport
• Maximizes entropy regularized welfare criterion
• Applies method to caseworker-job seeker matching