Multicalibration yields better matchings

2025-11-14

AI Summary

In weighted graph optimal matching, edge weights are often derived from imperfect predictive models rather than ground-truth values, leading to degraded performance of prediction-based matching algorithms. To address this, we propose leveraging multicalibration—a fairness-inspired notion requiring unbiased predictions across all structured subpopulations defined by context features—to mitigate prediction bias and enhance matching robustness. We design a unified framework that integrates multicalibrated predictors with standard matching algorithms and construct theoretically grounded calibration procedures via sample complexity analysis. We prove that matchings produced under multicalibrated predictions achieve provable competitive ratios relative to the oracle optimum, and we derive finite-sample upper bounds on the required calibration sample complexity—demonstrating both statistical efficiency and generalization under prediction uncertainty. Our key contribution is the first application of multicalibration to graph matching decision problems, enabling joint optimization of prediction fidelity and downstream decision quality.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Reasoning under Uncertainty: Graphical Models
• Constraint Satisfaction and Optimization: Other Foundations of Constraint Satisfaction

Application Category

• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking

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.

Problem

• Optimizing graph matching with imperfect weight predictors
• Ensuring predictor fairness through multicalibration techniques
• Competing with optimal decision rules using calibrated predictions

Innovation

• Multicalibration ensures predictor unbiasedness on protected sets
• Constructs multicalibrated predictor for competitive matching performance
• Provides sample complexity bounds for the proposed method