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Poster
A Game Theoretic Analysis of Additive Adversarial Attacks and Defenses
Ambar Pal · Rene Vidal

Wed Dec 09 09:00 AM -- 11:00 AM (PST) @ Poster Session 3 #909
in Poster Session 4 »

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 a 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.

Author Information

Ambar Pal (Johns Hopkins University)
Rene Vidal (Mathematical Institute for Data Science, Johns Hopkins University, USA)

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