A Theory of Universal Agnostic Learning

Steve Hanneke; Shay Moran

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arXiv · 2601.20961

A Theory of Universal Agnostic Learning

Steve Hanneke·Shay Moran

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Abstract

We provide a complete theory of optimal universal rates for binary classification in the agnostic setting. This extends the realizable-case theory of Bousquet, Hanneke, Moran, van Handel, and Yehudayoff (2021) by removing the realizability assumption on the distribution. We identify a fundamental tetrachotomy of optimal rates: for every concept class, the optimal universal rate of convergence of the excess error rate is one of $e^{-n}$, $e^{-o(n)}$, $o(n^{-1/2})$, or arbitrarily slow. We further identify simple combinatorial structures which determine which of these categories any given concept class falls into.

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Steve Hanneke, Shay Moran. 2026-01-28. A Theory of Universal Agnostic Learning. https://arxiv.org/abs/2601.20961

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