A Characterization of Semi-Supervised Adversarially Robust PAC Learnability

Part of Advances in Neural Information Processing Systems 35 (NeurIPS 2022) Main Conference Track

Bibtex Paper Supplemental


Idan Attias, Steve Hanneke, Yishay Mansour


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.