Black-Box Certification with Randomized Smoothing: A Functional Optimization Based Framework

02/21/2020 ∙ by Dinghuai Zhang, et al. ∙ 0

Randomized classifiers have been shown to provide a promising approach for achieving certified robustness against adversarial attacks in deep learning. However, most existing methods only leverage Gaussian smoothing noise and only work for ℓ_2 perturbation. We propose a general framework of adversarial certification with non-Gaussian noise and for more general types of attacks, from a unified functional optimization perspective. Our new framework allows us to identify a key trade-off between accuracy and robustness via designing smoothing distributions, helping to design new families of non-Gaussian smoothing distributions that work more efficiently for different ℓ_p settings, including ℓ_1, ℓ_2 and ℓ_∞ attacks. Our proposed methods achieve better certification results than previous works and provide a new perspective on randomized smoothing certification.

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