Regularization for Adversarial Robust Learning

• URL: http://arxiv.org/abs/2408.09672v2
• Date: Thu, 22 Aug 2024 10:07:50 GMT
• Title: Regularization for Adversarial Robust Learning
• Authors: Jie Wang, Rui Gao, Yao Xie,
• Abstract summary: We develop a novel approach to adversarial training that integrates $phi$-divergence regularization into the distributionally robust risk function. This regularization brings a notable improvement in computation compared with the original formulation. We validate our proposed method in supervised learning, reinforcement learning, and contextual learning and showcase its state-of-the-art performance against various adversarial attacks.
• Score: 18.46110328123008
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Despite the growing prevalence of artificial neural networks in real-world applications, their vulnerability to adversarial attacks remains a significant concern, which motivates us to investigate the robustness of machine learning models. While various heuristics aim to optimize the distributionally robust risk using the $\infty$-Wasserstein metric, such a notion of robustness frequently encounters computation intractability. To tackle the computational challenge, we develop a novel approach to adversarial training that integrates $\phi$-divergence regularization into the distributionally robust risk function. This regularization brings a notable improvement in computation compared with the original formulation. We develop stochastic gradient methods with biased oracles to solve this problem efficiently, achieving the near-optimal sample complexity. Moreover, we establish its regularization effects and demonstrate it is asymptotic equivalence to a regularized empirical risk minimization framework, by considering various scaling regimes of the regularization parameter and robustness level. These regimes yield gradient norm regularization, variance regularization, or a smoothed gradient norm regularization that interpolates between these extremes. We numerically validate our proposed method in supervised learning, reinforcement learning, and contextual learning and showcase its state-of-the-art performance against various adversarial attacks.

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