Adaptive versus Standard Descent Methods and Robustness Against Adversarial Examples
This addresses the problem of improving model robustness for machine learning practitioners, but it is incremental as it focuses on comparing existing optimization methods rather than introducing a new defense.
The paper investigates how optimization algorithms affect classifier robustness to adversarial examples, showing that adaptive methods can lead to worse robustness than non-adaptive methods in certain learning problems, with experimental evidence supporting this finding.
Adversarial examples are a pervasive phenomenon of machine learning models where seemingly imperceptible perturbations to the input lead to misclassifications for otherwise statistically accurate models. In this paper we study how the choice of optimization algorithm influences the robustness of the resulting classifier to adversarial examples. Specifically we show an example of a learning problem for which the solution found by adaptive optimization algorithms exhibits qualitatively worse robustness properties against both $L_{2}$- and $L_{\infty}$-adversaries than the solution found by non-adaptive algorithms. Then we fully characterize the geometry of the loss landscape of $L_{2}$-adversarial training in least-squares linear regression. The geometry of the loss landscape is subtle and has important consequences for optimization algorithms. Finally we provide experimental evidence which suggests that non-adaptive methods consistently produce more robust models than adaptive methods.