Fair and Welfare-Efficient Constrained Multi-matchings under Uncertainty

TL;DR

This paper develops methods for fair, welfare-efficient resource allocation under uncertainty, using machine learning to estimate utilities and balancing mean performance with predictive variance in stochastic and robust settings.

Contribution

It introduces a unified framework for constrained multi-matching under uncertainty, combining stochastic and robust optimization paradigms with fairness and welfare considerations.

Findings

Effective allocation strategies on conference reviewer datasets

Scalable methods for constrained resource allocation under uncertainty

Balances utility estimation accuracy with fairness objectives

Abstract

We study fair allocation of constrained resources, where a market designer optimizes overall welfare while maintaining group fairness. In many large-scale settings, utilities are not known in advance, but are instead observed after realizing the allocation. We therefore estimate agent utilities using machine learning. Optimizing over estimates requires trading-off between mean utilities and their predictive variances. We discuss these trade-offs under two paradigms for preference modeling -- in the stochastic optimization regime, the market designer has access to a probability distribution over utilities, and in the robust optimization regime they have access to an uncertainty set containing the true utilities with high probability. We discuss utilitarian and egalitarian welfare objectives, and we explore how to optimize for them under stochastic and robust paradigms. We demonstrate the efficacy of our approaches on three publicly available conference reviewer assignment datasets. The approaches presented enable scalable constrained resource allocation under uncertainty for many combinations of objectives and preference models.