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# Agnostic Learning

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arXiv Nov 4, 2026
Halfspace learning gets differential privacy for free: in three agnostic settings the privacy cost folds into the statistical term
For agnostically learning halfspaces with arbitrary labels under Gaussian marginals, computationally efficient differentially private algorithms were previously missing. This work reports efficient private learners in three settings, improper, proper and semi-agnostic; when the privacy parameter is at least the accuracy parameter, the extra sample cost of privacy is absorbed by each setting's non-private statistical term, making privacy free in sample complexity.
For agnostically learning halfspaces with arbitrary labels under Gaussian marginals, computationally efficient differentially private algorithms were previously missing. This work reports efficient private learners in three settings, improper, proper and semi-agnostic; when the privacy parameter is at least the accuracy parameter, the extra sample cost of privacy is absorbed by each setting's non-private statistical term, making privacy free in sample complexity.
University of Copenhagen
Giorgio Racca（First author）
Agnostic Learning Differential Privacy Halfspaces
arXiv Nov 4, 2026
Agnostic learning and multiaccuracy proved equivalent: one multiaccuracy oracle, queried adaptively, reaches the best discriminator
For a fixed feature distribution and an arbitrary model class, agnostic learning (training a discriminator that matches the best member of the class) and multiaccuracy (training a generator whose labels no observer in the class can distinguish from real ones) are proved equivalent in statistical and computational complexity. Only the direction from agnostic learning to multiaccuracy was known; the converse was blocked because a single multiaccurate predictor can fail to beat random guessing even after calibration. The new reduction repeatedly queries a multiaccuracy oracle, splits by prediction level sets and averages the iterates, yielding a predictor that is both multiaccurate and calibrated and thus performs agnostic learning.
For a fixed feature distribution and an arbitrary model class, agnostic learning (training a discriminator that matches the best member of the class) and multiaccuracy (training a generator whose labels no observer in the class can distinguish from real ones) are proved equivalent in statistical and computational complexity. Only the direction from agnostic learning to multiaccuracy was known; the converse was blocked because a single multiaccurate predictor can fail to beat random guessing even after calibration. The new reduction repeatedly queries a multiaccuracy oracle, splits by prediction level sets and averages the iterates, yielding a predictor that is both multiaccurate and calibrated and thus performs agnostic learning.
Stanford University Harvard University University of Oxford Apple (United States)
Sílvia Casacuberta（First author）
Agnostic Learning Multiaccuracy Oracle Reduction Multicalibration No-Regret Learning

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