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Adversarial Attack Generation Based on Min-Max Optimization

Adversarial Attack Generation Empowered by Min-Max Optimization

arXiv· arXiv:1906.03563· Jingkang Wang, Tianyun Zhang, Sijia Liu, Pin-Yu Chen, Jiacen Xu, Makan Fardad, Bo LiUniversity of Toronto; Vector Institute; Cleveland State University; Michigan State University; MIT-IBM Watson AI Lab, IBM Research; University of California, Irvine; Syracuse University; University of Illinois at Urbana-ChampaignIndexed by this site · 16 days ago· Originally publishedAttacks

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AI summaryThe researchers propose a general framework for adversarial attack generation based on min-max optimization, reformulating the minimization of the worst-case attack loss as a min-max problem that maximizes domain weights over multiple attack domains. The framework is applied uniformly to three types of attack generation: attacking model ensembles, designing universal perturbations across multiple inputs, and constructing attacks robust to data transformations. The authors state that experiments show the method significantly improves attack effectiveness over existing heuristic strategies and also yields robustness improvements over state-of-the-art defenses trained against multiple perturbation types; the adaptive domain weights learned from the framework can also be used to explain the attack difficulty of each domain. Code is open-sourced at https://github.com/wangjksjtu/minmax-adv。

Questions
Min-max optimization beyond adversarial training has not been systematically studied in attack generation; existing ensemble attacks, universal perturbations, and transformation-robust attacks mostly rely on heuristic weighting such as uniform averaging, which the authors argue causes performance loss.
Methods
Formulate minimizing the worst attack loss over multiple domains as a min-max problem: the domain weights w are maximized over the probability simplex with a quadratic regularization term, solved by alternating projected gradient descent-ascent (APGDA), with an O(1/T) convergence rate; it is also extended to multi-perturbation defense (AMPGD).
Experiments and results
On ensemble attacks, multi-image universal perturbations, and attacks robust to data transformations on MNIST/CIFAR-10, the authors report an average ASRall improvement of 17.48%–40.79%; for multi-lp perturbation defense, AMPGD's All Attacks robust accuracy is higher than MSD (MNIST 64.1% vs. 58.4%).
Limitations and future work
The paper has no dedicated limitations section; experiments cover only MNIST/CIFAR-10 image classification and 8 self-trained models, attacks are white-box lp-norm settings, and the number of repetitions and variance are not reported.

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