A Characterization of Semi-Supervised Adversarially Robust PAC Learnability

Idan Attias, Steve Hanneke, Yishay Mansour

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

Abstract:

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.