An Efficient Black-Box Reduction from Online Learning to Multicalibration, and a New Route to $Φ$-Regret Minimization

2026-04-21

AI Summary

This work addresses the efficient implementation of high-dimensional online multicalibration and establishes a streamlined reduction from external regret to Φ-regret. By integrating no-regret learners with solvers for expected variational inequalities (EVI), the authors develop a black-box reduction framework that, for the first time in general settings, achieves a √T regret bound while preserving oracle efficiency. This approach circumvents the intricate fixed-point machinery traditionally required, thereby unifying and extending existing Φ-regret minimization algorithms. Notably, it naturally accommodates discrepancy classes in reproducing kernel Hilbert spaces. The results resolve an open problem posed at SODA '24 and improve upon findings presented at STOC '25, with applicability to complex scenarios such as delayed feedback, censored outcomes, and multi-class full prediction.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• 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
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs

Abstract

We give a Gordon-Greenwald-Marks (GGM) style black-box reduction from online learning to online multicalibration. Concretely, we show that to achieve high-dimensional multicalibration with respect to a class of functions H, it suffices to combine any no-regret learner over H with an expected variational inequality (EVI) solver. We also prove a converse statement showing that efficient multicalibration implies efficient EVI solving, highlighting how EVIs in multicalibration mirror the role of fixed points in the GGM result for $Φ$-regret. This first set of results resolves the main open question in Garg, Jung, Reingold, and Roth (SODA '24), showing that oracle-efficient online multicalibration with $\sqrt{T}$-type guarantees is possible in full generality. Furthermore, our GGM-style reduction unifies the analyses of existing online multicalibration algorithms, enables new algorithms for challenging environments with delayed observations or censored outcomes, and yields the first efficient black-box reduction between online learning and multiclass omniprediction. Our second main result is a fine-grained reduction from high-dimensional online multicalibration to (contextual) $Φ$-regret minimization. Together with our first result, this establishes a new route from external regret to Phi-regret that bypasses sophisticated fixed-point or semi-separation machinery, dramatically simplifies a result of Daskalakis, Farina, Fishelson, Pipis, and Schneider (STOC '25) while improving rates, and yields new algorithms that are robust to richer deviation classes, such as those belonging to any reproducing kernel Hilbert space.

Problem

• online learning
• multicalibration
• Φ-regret minimization
• black-box reduction
• expected variational inequality

Innovation

• black-box reduction
• online multicalibration
• Φ-regret minimization
• expected variational inequality
• no-regret learning