A PAC-Bayes Analysis of Adversarial Robustness
Paul Viallard, Guillaume Eric VIDOT, Amaury Habrard, Emilie Morvant
Abstract
We propose the first general PAC-Bayesian generalization bounds for adversarial robustness, that estimate, at test time, how much a model will be invariant to imperceptible perturbations in the input. Instead of deriving a worst-case analysis of the risk of a hypothesis over all the possible perturbations, we leverage the PAC-Bayesian framework to bound the averaged risk on the perturbations for majority votes (over the whole class of hypotheses). Our theoretically founded analysis has the advantage to provide general bounds (i) that are valid for any kind of attacks (i.e., the adversarial attacks), (ii) that are tight thanks to the PAC-Bayesian framework, (iii) that can be directly minimized during the learning phase to obtain a robust model on different attacks at test time.
BibTeX
@inproceedings{
viallard2021a,
title={A {PAC}-Bayes Analysis of Adversarial Robustness},
author={Paul Viallard and Guillaume Eric VIDOT and Amaury Habrard and Emilie Morvant},
booktitle={Advances in Neural Information Processing Systems},
editor={A. Beygelzimer and Y. Dauphin and P. Liang and J. Wortman Vaughan},
year={2021},
url={https://openreview.net/forum?id=sUBSPowU3L5}
}