Improving the Tightness of Convex Relaxation Bounds for Training Certifiably Robust Classifiers

Authors: Chen Zhu, Renkun Ni, Ping-yeh Chiang, Hengduo Li, Furong Huang, Tom Goldstein
Published: 2020-02-22

Source: https://arxiv.org/abs/2002.09766

PDF: https://arxiv.org/pdf/2002.09766

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ロバスト性評価 最適化問題 正則化

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Abstract

Convex relaxations are effective for training and certifying neural networks against norm-bounded adversarial attacks, but they leave a large gap between certifiable and empirical robustness. In principle, convex relaxation can provide tight bounds if the solution to the relaxed problem is feasible for the original non-convex problem. We propose two regularizers that can be used to train neural networks that yield tighter convex relaxation bounds for robustness. In all of our experiments, the proposed regularizers result in higher certified accuracy than non-regularized baselines.