A Characterization of Semi-Supervised Adversarially Robust PAC Learnability

Idan Attias · Steve Hanneke · Yishay Mansour

Hall J (level 1) #810

Keywords: [ Partial Concept Classes ] [ PAC Learning ] [ Combinatorial Dimensions ] [ Sample Complexity ] [ Adversarial Robustness ] [ Semi-Supervised Learning ]


We study the problem of learning an adversarially robust predictor to test time attacks in the semi-supervised PAC model.We address the question of how many labeled and unlabeled examples are required to ensure learning.We show that having enough unlabeled data (the size of a labeled sample that a fully-supervised method would require),the labeled sample complexity can be arbitrarily smaller compared to previous works, and is sharply characterized by a different complexity measure. We prove nearly matching upper and lower bounds on this sample complexity.This shows that there is a significant benefit in semi-supervised robust learning even in the worst-case distribution-free model, and establishes a gap between supervised and semi-supervised label complexities which is known not to hold in standard non-robust PAC learning.

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