Simultaneous Blackwell Approachability and Applications to Multiclass Omniprediction

2026-02-19

AI Summary

This work addresses the problem of multiclass omniprediction—simultaneously achieving suboptimality guarantees over an infinite class of comparators and a family of loss functions. Moving beyond prior studies restricted to binary classification, we introduce a novel Blackwell approachability framework tailored for k-class prediction. By leveraging potential-based methods and coupled action strategies, our approach unifies statistical and online learning settings, enabling simultaneous approximation of multiple target sets. We establish that ε-omniprediction is achievable in the k-class setting with sample complexity or regret bounds scaling as O(ε^{-(k+1)}), thereby substantially extending the theoretical foundations of omniprediction.

Technology Category

• Machine Learning: Online Learning & Bandits
• Game Theory and Economic Paradigms: Adversarial Learning
• Humans and AI: Human-Aware Planning and Behavior Prediction

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

Omniprediction is a learning problem that requires suboptimality bounds for each of a family of losses $\mathcal{L}$ against a family of comparator predictors $\mathcal{C}$. We initiate the study of omniprediction in a multiclass setting, where the comparator family $\mathcal{C}$ may be infinite. Our main result is an extension of the recent binary omniprediction algorithm of [OKK25] to the multiclass setting, with sample complexity (in statistical settings) or regret horizon (in online settings) $\approx \varepsilon^{-(k+1)}$, for $\varepsilon$-omniprediction in a $k$-class prediction problem. En route to proving this result, we design a framework of potential broader interest for solving Blackwell approachability problems where multiple sets must simultaneously be approached via coupled actions.

Problem

• omniprediction
• multiclass
• Blackwell approachability
• suboptimality bounds
• comparator predictors

Innovation

• multiclass omniprediction
• Blackwell approachability
• simultaneous approachability
• sample complexity
• online learning