Multicalibration yields better matchings

TL;DR

This paper introduces multicalibration as a method to improve matching decisions under imperfect predictions by ensuring unbiasedness across protected sets, leading to more competitive matchings.

Contribution

It proposes a multicalibration technique for predictors that guarantees near-optimal matchings compared to any algorithm in a given class, with sample complexity bounds.

Findings

Multicalibration improves matching decisions under imperfect predictors.

Constructed multicalibrated predictor is competitive with the best decision rule.

Provides sample complexity bounds for the proposed method.

Abstract

Consider the problem of finding the best matching in a weighted graph where we only have access to predictions of the actual stochastic weights, based on an underlying context. If the predictor is the Bayes optimal one, then computing the best matching based on the predicted weights is optimal. However, in practice, this perfect information scenario is not realistic. Given an imperfect predictor, a suboptimal decision rule may compensate for the induced error and thus outperform the standard optimal rule. In this paper, we propose multicalibration as a way to address this problem. This fairness notion requires a predictor to be unbiased on each element of a family of protected sets of contexts. Given a class of matching algorithms $\mathcal C$ and any predictor $\gamma$ of the edge-weights, we show how to construct a specific multicalibrated predictor $\hat \gamma$, with the following property. Picking the best matching based on the output of $\hat \gamma$ is competitive with the best decision rule in $\mathcal C$ applied onto the original predictor $\gamma$. We complement this result by providing sample complexity bounds.