On the Loss Landscape of Adversarial Training: Identifying Challenges and How to Overcome Them

TL;DR

This paper investigates how adversarial training affects the loss landscape of machine learning models, revealing challenges like increased curvature and scattered gradients, and proposes a periodic adversarial scheduling strategy to improve training outcomes.

Contribution

The paper provides analytical and numerical insights into the loss landscape under adversarial training and introduces PAS to mitigate associated optimization challenges.

Findings

Adversarial loss landscapes have higher curvature and scattered gradients.

Large adversarial budgets hinder escape from suboptimal initializations.

PAS improves training robustness and reduces sensitivity to learning rate.

Abstract

We analyze the influence of adversarial training on the loss landscape of machine learning models. To this end, we first provide analytical studies of the properties of adversarial loss functions under different adversarial budgets. We then demonstrate that the adversarial loss landscape is less favorable to optimization, due to increased curvature and more scattered gradients. Our conclusions are validated by numerical analyses, which show that training under large adversarial budgets impede the escape from suboptimal random initialization, cause non-vanishing gradients and make the model find sharper minima. Based on these observations, we show that a periodic adversarial scheduling (PAS) strategy can effectively overcome these challenges, yielding better results than vanilla adversarial training while being much less sensitive to the choice of learning rate.