VC Classes are Adversarially Robustly Learnable, but Only Improperly
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We study the question of learning an adversarially robust predictor. We show that any hypothesis class H with finite VC dimension is robustly PAC learnable with an improper learning rule. The requirement of being improper is necessary as we exhibit examples of hypothesis classes H with finite VC dimension that are not robustly PAC learnable with any proper learning rule.
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