Simultaneous Blackwell Approachability and Applications to Multiclass Omniprediction

TL;DR

This paper extends the concept of omniprediction to multiclass problems, providing an algorithm with sample complexity or regret bounds that scale with the number of classes, and introduces a new approach for solving complex Blackwell approachability problems.

Contribution

It develops a multiclass omniprediction algorithm with near-optimal bounds and introduces a novel framework for simultaneous Blackwell approachability of multiple sets.

Findings

Extended binary omniprediction algorithm to multiclass setting.

Achieved sample complexity or regret bounds of approximately ε^{-(k+1)}.

Designed a new framework for coupled Blackwell approachability problems.

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.