Mind the Box: $l_1$-APGD for Sparse Adversarial Attacks on Image Classifiers

Francesco Croce, Matthias Hein
Proceedings of the 38th International Conference on Machine Learning, PMLR 139:2201-2211, 2021.

Abstract

We show that when taking into account also the image domain $[0,1]^d$, established $l_1$-projected gradient descent (PGD) attacks are suboptimal as they do not consider that the effective threat model is the intersection of the $l_1$-ball and $[0,1]^d$. We study the expected sparsity of the steepest descent step for this effective threat model and show that the exact projection onto this set is computationally feasible and yields better performance. Moreover, we propose an adaptive form of PGD which is highly effective even with a small budget of iterations. Our resulting $l_1$-APGD is a strong white-box attack showing that prior works overestimated their $l_1$-robustness. Using $l_1$-APGD for adversarial training we get a robust classifier with SOTA $l_1$-robustness. Finally, we combine $l_1$-APGD and an adaptation of the Square Attack to $l_1$ into $l_1$-AutoAttack, an ensemble of attacks which reliably assesses adversarial robustness for the threat model of $l_1$-ball intersected with $[0,1]^d$.

Cite this Paper

BibTeX
@InProceedings{pmlr-v139-croce21a, title = {Mind the Box: $l_1$-APGD for Sparse Adversarial Attacks on Image Classifiers}, author = {Croce, Francesco and Hein, Matthias}, booktitle = {Proceedings of the 38th International Conference on Machine Learning}, pages = {2201--2211}, year = {2021}, editor = {Meila, Marina and Zhang, Tong}, volume = {139}, series = {Proceedings of Machine Learning Research}, month = {18--24 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v139/croce21a/croce21a.pdf}, url = {https://proceedings.mlr.press/v139/croce21a.html}, abstract = {We show that when taking into account also the image domain $[0,1]^d$, established $l_1$-projected gradient descent (PGD) attacks are suboptimal as they do not consider that the effective threat model is the intersection of the $l_1$-ball and $[0,1]^d$. We study the expected sparsity of the steepest descent step for this effective threat model and show that the exact projection onto this set is computationally feasible and yields better performance. Moreover, we propose an adaptive form of PGD which is highly effective even with a small budget of iterations. Our resulting $l_1$-APGD is a strong white-box attack showing that prior works overestimated their $l_1$-robustness. Using $l_1$-APGD for adversarial training we get a robust classifier with SOTA $l_1$-robustness. Finally, we combine $l_1$-APGD and an adaptation of the Square Attack to $l_1$ into $l_1$-AutoAttack, an ensemble of attacks which reliably assesses adversarial robustness for the threat model of $l_1$-ball intersected with $[0,1]^d$.} }
Endnote
%0 Conference Paper %T Mind the Box: $l_1$-APGD for Sparse Adversarial Attacks on Image Classifiers %A Francesco Croce %A Matthias Hein %B Proceedings of the 38th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2021 %E Marina Meila %E Tong Zhang %F pmlr-v139-croce21a %I PMLR %P 2201--2211 %U https://proceedings.mlr.press/v139/croce21a.html %V 139 %X We show that when taking into account also the image domain $[0,1]^d$, established $l_1$-projected gradient descent (PGD) attacks are suboptimal as they do not consider that the effective threat model is the intersection of the $l_1$-ball and $[0,1]^d$. We study the expected sparsity of the steepest descent step for this effective threat model and show that the exact projection onto this set is computationally feasible and yields better performance. Moreover, we propose an adaptive form of PGD which is highly effective even with a small budget of iterations. Our resulting $l_1$-APGD is a strong white-box attack showing that prior works overestimated their $l_1$-robustness. Using $l_1$-APGD for adversarial training we get a robust classifier with SOTA $l_1$-robustness. Finally, we combine $l_1$-APGD and an adaptation of the Square Attack to $l_1$ into $l_1$-AutoAttack, an ensemble of attacks which reliably assesses adversarial robustness for the threat model of $l_1$-ball intersected with $[0,1]^d$.
APA
Croce, F. & Hein, M.. (2021). Mind the Box: $l_1$-APGD for Sparse Adversarial Attacks on Image Classifiers. Proceedings of the 38th International Conference on Machine Learning, in Proceedings of Machine Learning Research 139:2201-2211 Available from https://proceedings.mlr.press/v139/croce21a.html.

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