Poster
A Characterization of Semi-Supervised Adversarially Robust PAC Learnability
Idan Attias · Steve Hanneke · Yishay Mansour
Hall J (level 1) #810
Keywords: [ Semi-Supervised Learning ] [ Adversarial Robustness ] [ Sample Complexity ] [ Combinatorial Dimensions ] [ PAC Learning ] [ Partial Concept Classes ]
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.