A Game Theoretic Analysis of Additive Adversarial Attacks and Defenses
This provides a theoretical foundation for understanding equilibrium conditions in adversarial learning, which is incremental but addresses a key open problem in the field.
The paper tackles the problem of determining conditions for stable adversarial attacks and defenses in machine learning, proving that the Fast Gradient Method attack and Randomized Smoothing defense form a Nash Equilibrium under a locally linear decision boundary model, with a generalization bound provided for approximating this equilibrium from finite data.
Research in adversarial learning follows a cat and mouse game between attackers and defenders where attacks are proposed, they are mitigated by new defenses, and subsequently new attacks are proposed that break earlier defenses, and so on. However, it has remained unclear as to whether there are conditions under which no better attacks or defenses can be proposed. In this paper, we propose a game-theoretic framework for studying attacks and defenses which exist in equilibrium. Under a locally linear decision boundary model for the underlying binary classifier, we prove that the Fast Gradient Method attack and the Randomized Smoothing defense form a Nash Equilibrium. We then show how this equilibrium defense can be approximated given finitely many samples from a data-generating distribution, and derive a generalization bound for the performance of our approximation.