How Global Calibration Strengthens Multiaccuracy

2025-04-21

AI Summary

This paper investigates the synergistic enhancement of multi-group fairness in prediction by jointly leveraging multiaccuracy and global calibration. We propose the novel paradigm of “calibrated multiaccuracy,” and establish, for the first time, that global calibration can amplify weak multiaccuracy to strength equivalent to multicalibration—thereby enabling a strict reduction to strong agnostic learning and yielding an optimal density hardcore distribution. Methodologically, we integrate tools from agnostic learning theory, multi-group fairness analysis, hardcore lemma derivation, and weighted predictor construction. Our main contributions are: (1) a formal characterization of the synergistic gain mechanism between multiaccuracy and global calibration; (2) breakthroughs in theoretical barriers concerning weak-learner recovery and hardcore density optimization; and (3) a precise delineation of the capability boundaries of multiaccuracy and weak agnostic learning. Collectively, these results provide a more robust and formally justified theoretical foundation for fair machine learning.

Technology Category

• Machine Learning: Calibration & Uncertainty Quantification
• Game Theory and Economic Paradigms: Adversarial Learning
• Multiagent Systems: Multiagent Learning

Application Category

• 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
• Economics, Online Markets and Human Computation: Fairness, privacy, and diversity in economic environments

Abstract

Multiaccuracy and multicalibration are multigroup fairness notions for prediction that have found numerous applications in learning and computational complexity. They can be achieved from a single learning primitive: weak agnostic learning. Here we investigate the power of multiaccuracy as a learning primitive, both with and without the additional assumption of calibration. We find that multiaccuracy in itself is rather weak, but that the addition of global calibration (this notion is called calibrated multiaccuracy) boosts its power substantially, enough to recover implications that were previously known only assuming the stronger notion of multicalibration. We give evidence that multiaccuracy might not be as powerful as standard weak agnostic learning, by showing that there is no way to post-process a multiaccurate predictor to get a weak learner, even assuming the best hypothesis has correlation $1/2$. Rather, we show that it yields a restricted form of weak agnostic learning, which requires some concept in the class to have correlation greater than $1/2$ with the labels. However, by also requiring the predictor to be calibrated, we recover not just weak, but strong agnostic learning. A similar picture emerges when we consider the derivation of hardcore measures from predictors satisfying multigroup fairness notions. On the one hand, while multiaccuracy only yields hardcore measures of density half the optimal, we show that (a weighted version of) calibrated multiaccuracy achieves optimal density. Our results yield new insights into the complementary roles played by multiaccuracy and calibration in each setting. They shed light on why multiaccuracy and global calibration, although not particularly powerful by themselves, together yield considerably stronger notions.

Problem

• Investigates multiaccuracy's power with/without calibration in fairness.
• Shows calibrated multiaccuracy boosts learning power significantly.
• Explores multiaccuracy's limitations versus standard weak agnostic learning.

Innovation

• Global calibration boosts multiaccuracy power
• Calibrated multiaccuracy enables strong agnostic learning
• Weighted calibrated multiaccuracy achieves optimal density