Understanding the Role of Adversarial Regularization in Supervised Learning

TL;DR

This paper investigates the theoretical foundations of adversarial regularization in supervised learning, analyzing its convergence, gradient flow, and generalization, supported by empirical evidence of its acceleration effects.

Contribution

It provides a theoretical analysis of adversarial regularization's performance, including convergence and generalization, and questions existing capacity-based bounds in this context.

Findings

Adversarial regularization accelerates gradient descent.

Existing capacity bounds may not fully explain generalization in adversarial learning.

Distinct behaviors observed in neural embedded vector spaces under adversarial training.

Abstract

Despite numerous attempts sought to provide empirical evidence of adversarial regularization outperforming sole supervision, the theoretical understanding of such phenomena remains elusive. In this study, we aim to resolve whether adversarial regularization indeed performs better than sole supervision at a fundamental level. To bring this insight into fruition, we study vanishing gradient issue, asymptotic iteration complexity, gradient flow and provable convergence in the context of sole supervision and adversarial regularization. The key ingredient is a theoretical justification supported by empirical evidence of adversarial acceleration in gradient descent. In addition, motivated by a recently introduced unit-wise capacity based generalization bound, we analyze the generalization error in adversarial framework. Guided by our observation, we cast doubts on the ability of this measure to explain generalization. We therefore leave as open questions to explore new measures that can explain generalization behavior in adversarial learning. Furthermore, we observe an intriguing phenomenon in the neural embedded vector space while contrasting adversarial learning with sole supervision.