Multicalibration Yields Better Matchings

arXiv:2511.11413v2 Announce Type: replace 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, and by performing numerical experiments.

Source: arXiv cs.LG | 2026-08-06