Certified Adversarial Robustness Within Multiple Perturbation Bounds

Abstract

Randomized smoothing (RS) is a well known certified defense against adversarial attacks, which creates a smoothed classifier by predicting the most likely class under random noise perturbations of inputs during inference. While initial work focused on robustness to ℓ2 norm perturbations using noise sampled from a Gaussian distribution, subsequent works have shown that different noise distributions can result in robustness to other ℓp norm bounds as well. In general, a specific noise distribution is optimal for defending against a given ℓp norm based attack. In this work, we aim to improve the certified adversarial robustness against multiple perturbation bounds simultaneously. Towards this, we firstly present a novel certification scheme, that effectively combines the certificates obtained using different noise distributions to obtain optimal results against multiple perturbation bounds. We further propose a novel training noise distribution along with a regularized training scheme to improve the certification within both ℓ1 and ℓ2 perturbation norms simultaneously. Contrary to prior works, we compare the certified robustness of different training algorithms across the same natural (clean) accuracy, rather than across fixed noise levels used for training and certification. We also empirically invalidate the argument that training and certifying the classifier with the same amount of noise gives the best results. The proposed approach achieves improvements on the ACR (Average Certified Radius) metric across both ℓ1 and ℓ2 perturbation bounds. Code available at https://github.com/valiisc/NU-Certified-Robustness