On the Connection between Differential Privacy and Adversarial Robustness in Machine Learning

Adversarial examples in machine learning has been a topic of intense research interest, with attacks and defenses being developed in a tight back-and-forth. Most past defenses are best-effort, heuristic approaches that have all been shown to be vulnerable to sophisticated attacks. More recently, rigorous defenses that provide formal guarantees have emerged, but are hard to scale or generalize. A rigorous and general foundation for designing defenses is required to get us off this arms race trajectory. We propose leveraging differential privacy (DP) as a formal building block for robustness against adversarial examples. We observe that the semantic of DP is closely aligned with the formal definition of robustness to adversarial examples. We propose PixelDP, a strategy for learning robust deep neural networks based on formal DP guarantees. PixelDP networks give theoretical guarantees for a subset of their predictions regarding the robustness against adversarial perturbations of bounded size. Our evaluation with MNIST, CIFAR-10, and CIFAR-100 shows that PixelDP networks achieve accuracy under attack on par with the best-performing defense to date, but additionally certify robustness against meaningful-size 1-norm and 2-norm attacks for 40-60% of their predictions. Our experience points to DP as a rigorous, broadly applicable, and mechanism-rich foundation for robust machine learning.