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arXiv 2102.05475cs.LGcs.CR
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对抗性鲁棒性:你的傻瓜让你更强大

Adversarial Robustness: What fools you makes you stronger

School of Computer and Communication Sciences, EPFL(EPFL计算机与通信科学学院)

Grzegorz Głuch, Rüdiger Urbanke

摘要:

我们证明了标准PAC学习模型和等价查询学习模型之间的样本复杂度的指数分离。然后,我们证明了这种分离对对抗鲁棒性有着有趣的影响。我们探索设计一个自适应防御的愿景,在攻击者的存在下计算一个模型,可证明是强大的。特别是,我们展示了如何在一个简化的设置实现这一愿景。为了做到这一点,我们引入了一个强大对手的概念:他不受他可以应用的扰动类型的限制,但是当使用分类器时,可以重复生成不同的对抗性示例。我们解释为什么这个概念是有趣的研究和使用它来证明以下内容。存在一种有效的类似对抗学习的方案,使得对于每个强大的对手$\mathbf{A}$,它输出一个分类器,该分类器(a)不能被$\mathbf{A}$强烈攻击,或者(b)具有至多$ε$的错误。在这两种情况下,我们的计划使用指数(在$ε$)更少的样本比PAC绑定所需的。

英文摘要:

We prove an exponential separation for the sample complexity between the standard PAC-learning model and a version of the Equivalence-Query-learning model. We then show that this separation has interesting implications for adversarial robustness. We explore a vision of designing an adaptive defense that in the presence of an attacker computes a model that is provably robust. In particular, we show how to realize this vision in a simplified setting. In order to do so, we introduce a notion of a strong adversary: he is not limited by the type of perturbations he can apply but when presented with a classifier can repetitively generate different adversarial examples. We explain why this notion is interesting to study and use it to prove the following. There exists an efficient adversarial-learning-like scheme such that for every strong adversary $\mathbf{A}$ it outputs a classifier that (a) cannot be strongly attacked by $\mathbf{A}$, or (b) has error at most $ε$. In both cases our scheme uses exponentially (in $ε$) fewer samples than what the PAC bound requires.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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