VC Classes are Adversarially Robustly Learnable, but Only Improperly
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Proceedings of the ThirtySecond Conference on Learning Theory, PMLR 99:25122530, 2019.
Abstract
We study the question of learning an adversarially robust predictor. We show that any hypothesis class $\mathcal{H}$ with finite VC dimension is robustly PAC learnable with an \emph{improper} learning rule. The requirement of being improper is necessary as we exhibit examples of hypothesis classes $\mathcal{H}$ with finite VC dimension that are \emph{not} robustly PAC learnable with any \emph{proper} learning rule.
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