Understanding and Improving Ensemble Adversarial Defense

The strategy of ensemble has become popular in adversarial defense, which trains multiple base classifiers to defend against adversarial attacks in a cooperative manner. Despite the empirical success, theoretical explanations on why an ensemble of adversarially trained classifiers is more robust than single ones remain unclear. To fill in this gap, we develop a new error theory dedicated to understanding ensemble adversarial defense, demonstrating a provable 0-1 loss reduction on challenging sample sets in an adversarial defense scenario. Guided by this theory, we propose an effective approach to improve ensemble adversarial defense, named interactive global adversarial training (iGAT). The proposal includes (1) a probabilistic distributing rule that selectively allocates to different base classifiers adversarial examples that are globally challenging to the ensemble, and (2) a regularization term to rescue the severest weaknesses of the base classifiers. Being tested over various existing ensemble adversarial defense techniques, iGAT is capable of boosting their performance by increases up to 17% evaluated using CIFAR10 and CIFAR100 datasets under both white-box and black-box attacks.

Faster Riemannian Newton-type Optimization by Subsampling and Cubic Regularization

This work is on constrained large-scale non-convex optimization where the constraint set implies a manifold structure. Solving such problems is important in a multitude of fundamental machine learning tasks. Recent advances on Riemannian optimization have enabled the convenient recovery of solutions by adapting unconstrained optimization algorithms over manifolds. However, it remains challenging to scale up and meanwhile maintain stable convergence rates and handle saddle points. We propose a new second-order Riemannian optimization algorithm, aiming at improving convergence rate and reducing computational cost. It enhances the Riemannian trust-region algorithm that explores curvature information to escape saddle points through a mixture of subsampling and cubic regularization techniques. We conduct rigorous analysis to study the convergence behavior of the proposed algorithm. We also perform extensive experiments to evaluate it based on two general machine learning tasks using multiple datasets. The proposed algorithm exhibits improved computational speed and convergence behavior compared to a large set of state-of-the-art Riemannian optimization algorithms.