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.

本文采用博弈论视角研究分类器对抗攻击的鲁棒性，证明了在确定性情况下不存在一个能保证最优鲁棒性的纳什均衡点，并提出了采用随机化方法构建具有鲁棒性的分类器的算法，实验结果验证了该方法的有效性。

随机化很重要：如何抵御强大的对抗性攻击

Randomization matters. How to defend against strong adversarial attacks

We present a systematic approach for achieving fairness in a binary
classification setting. While we focus on two well-known quantitative
definitions of fairness, our approach encompasses many other previously studied
definitions as special cases. The key idea is to reduce fair classification to
a sequence of cost-sensitive classification problems, whose solutions yield a
randomized classifier with the lowest (empirical) error subject to the desired
constraints. We introduce two reductions that work for any representation of
the cost-sensitive classifier and compare favorably to prior baselines on a
variety of data sets, while overcoming several of their disadvantages.

本文介绍了一个系统方法来在二元分类问题中实现公正性，该方法涵盖了许多先前研究的定义，将公平分类问题转化为成本敏感的分类问题序列，并引入两个新的降低方法来获得较优结果。