Constrained Gradient Descent: A Powerful and Principled Evasion Attack Against Neural Networks
Weiran Lin, Keane Lucas, Lujo Bauer, Michael K. Reiter, Mahmood Sharif
Abstract
We propose new, more efficient targeted white-box attacks against deep neural networks. Our attacks better align with the attacker’s goal: (1) tricking a model to assign higher probability to the target class than to any other class, while (2) staying within an $\epsilon$-distance of the attacked input. First, we demonstrate a loss function that explicitly encodes (1) and show that Auto-PGD finds more attacks with it. Second, we propose a new attack method, Constrained Gradient Descent (CGD), using a refinement of our loss function that captures both (1) and (2). CGD seeks to satisfy both attacker objectives—misclassification and bounded $\ell_{p}$-norm—in a principled manner, as part of the optimization, instead of via ad hoc post-processing techniques (e.g., projection or clipping). We show that CGD is more successful on CIFAR10 (0.9–4.2%) and ImageNet (8.6–13.6%) than state-of-the-art attacks while consuming less time (11.4–18.8%). Statistical tests confirm that our attack outperforms others against leading defenses on different datasets and values of $\epsilon$.
BibTeX
@InProceedings{pmlr-v162-lin22e,
title = {Constrained Gradient Descent: A Powerful and Principled Evasion Attack Against Neural Networks},
author = {Lin, Weiran and Lucas, Keane and Bauer, Lujo and Reiter, Michael K. and Sharif, Mahmood},
booktitle = {Proceedings of the 39th International Conference on Machine Learning},
pages = {13405--13430},
year = {2022},
editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan},
volume = {162},
series = {Proceedings of Machine Learning Research},
month = {17--23 Jul},
publisher = {PMLR},
pdf = {https://proceedings.mlr.press/v162/lin22e/lin22e.pdf},
url = {https://proceedings.mlr.press/v162/lin22e.html},
abstract = {We propose new, more efficient targeted white-box attacks against deep neural networks. Our attacks better align with the attacker’s goal: (1) tricking a model to assign higher probability to the target class than to any other class, while (2) staying within an $\epsilon$-distance of the attacked input. First, we demonstrate a loss function that explicitly encodes (1) and show that Auto-PGD finds more attacks with it. Second, we propose a new attack method, Constrained Gradient Descent (CGD), using a refinement of our loss function that captures both (1) and (2). CGD seeks to satisfy both attacker objectives—misclassification and bounded $\ell_{p}$-norm—in a principled manner, as part of the optimization, instead of via ad hoc post-processing techniques (e.g., projection or clipping). We show that CGD is more successful on CIFAR10 (0.9–4.2%) and ImageNet (8.6–13.6%) than state-of-the-art attacks while consuming less time (11.4–18.8%). Statistical tests confirm that our attack outperforms others against leading defenses on different datasets and values of $\epsilon$.}
}