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arXiv 2002.11565cs.LGcs.CRstat.ML

Randomization matters. How to defend against strong adversarial attacks

Université Paris-Dauphine, PSL Research University(巴黎多芬大学,PSL研究大学);CNRS(法国国家科学研究中心);Institut LIST, CEA(法国原子能与替代能源委员会列表研究所);Université Paris-Saclay(巴黎萨克雷大学)

Rafael Pinot, Raphael Ettedgui, Geovani Rizk, Yann Chevaleyre, Jamal Atif

英文摘要:

Is there a classifier that ensures optimal robustness against all adversarial attacks? This paper answers this question by adopting a game-theoretic point of view. We show that adversarial attacks and defenses form an infinite zero-sum game where classical results (e.g. Sion theorem) do not apply. We demonstrate the non-existence of a Nash equilibrium in our game when the classifier and the Adversary are both deterministic, hence giving a negative answer to the above question in the deterministic regime. Nonetheless, the question remains open in the randomized regime. We tackle this problem by showing that, undermild conditions on the dataset distribution, any deterministic classifier can be outperformed by a randomized one. This gives arguments for using randomization, and leads us to a new algorithm for building randomized classifiers that are robust to strong adversarial attacks. Empirical results validate our theoretical analysis, and show that our defense method considerably outperforms Adversarial Training against state-of-the-art attacks.

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