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Depending on how much information an adversary can access to, adversarialattacks can be classified as white-box attack and black-box attack. Forwhite-box attack, optimization-based attack algorithms such as projectedgradient descent (PGD) can achieve relatively high attack success rates withinmoderate iterates. However, they tend to generate adversarial examples near orupon the boundary of the perturbation set, resulting in large distortion.Furthermore, their corresponding black-box attack algorithms also suffer fromhigh query complexities, thereby limiting their practical usefulness. In thispaper, we focus on the problem of developing efficient and effectiveoptimization-based adversarial attack algorithms. In particular, we propose anovel adversarial attack framework for both white-box and black-box settingsbased on a variant of Frank-Wolfe algorithm. We show in theory that theproposed attack algorithms are efficient with an $O(1/\sqrt{T})$ convergencerate. The empirical results of attacking the ImageNet and MNIST datasets alsoverify the efficiency and effectiveness of the proposed algorithms. Morespecifically, our proposed algorithms attain the best attack performances inboth white-box and black-box attacks among all baselines, and are more time andquery efficient than the state-of-the-art.

A Frank-Wolfe Framework for Efficient and Effective Adversarial Attacks