Certifiable Distributional Robustness with Principled Adversarial Training


Nov 03, 2017 (modified: Nov 03, 2017) ICLR 2018 Conference Blind Submission readers: everyone Show Bibtex
  • Abstract: Neural networks are vulnerable to adversarial examples and researchers have proposed many heuristic attack and defense mechanisms. We take the principled view of distributionally robust optimization, which guarantees performance under adversarial input perturbations. By considering a Lagrangian penalty formulation of perturbation of the underlying data distribution in a Wasserstein ball, we provide a training procedure that augments model parameter updates with worst-case perturbations of training data. For smooth losses, our procedure provably achieves moderate levels of robustness with little computational or statistical cost relative to empirical risk minimization. Furthermore, our statistical guarantees allow us to efficiently certify robustness for the population loss. We match or outperform heuristic approaches on supervised and reinforcement learning tasks.
  • TL;DR: We provide a fast, principled adversarial training procedure with computational and statistical performance guarantees.
  • Keywords: adversarial training, distributionally robust optimization, deep learning, optimization, learning theory