Nash Equilibria and Pitfalls of Adversarial Training in Adversarial Robustness Games Article Swipe

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Adversarial system Best response Nash equilibrium Robustness (evolution) Computer science Classifier (UML) Fictitious play Artificial intelligence Zero-sum game Mathematical optimization Mathematical economics Machine learning Mathematics Biochemistry Gene Chemistry

Maria-Florina Balcan , Rattana Pukdee , Pradeep Ravikumar , Hongyang Zhang ·

YOU? · · 2022 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2210.12606 · OA: W4307311838

Adversarial training is a standard technique for training adversarially robust models. In this paper, we study adversarial training as an alternating best-response strategy in a 2-player zero-sum game. We prove that even in a simple scenario of a linear classifier and a statistical model that abstracts robust vs. non-robust features, the alternating best response strategy of such game may not converge. On the other hand, a unique pure Nash equilibrium of the game exists and is provably robust. We support our theoretical results with experiments, showing the non-convergence of adversarial training and the robustness of Nash equilibrium.