论文标题
对抗性稳健的学习：一种通用的最小值最佳学习者和表征
Adversarially Robust Learning: A Generic Minimax Optimal Learner and Characterization
论文作者
论文摘要
我们为在测试时间内对对抗性示例进行了学习预测的问题，为学习预测的问题提供了最小的最佳学习者。有趣的是，我们发现这需要新的算法思想和方法来实现对抗性的学习。特别是，我们从强烈的负面意义上表明，蒙塔瑟（Montasser），Hanneke和Srebro（2019）提出的强大学习者的次级临时性以及我们确定为本地学习者的更广泛的学习者。我们的结果是通过通过关键技术贡献采用全球视角来实现的：可能具有独立感兴趣的全球单包含图，它概括了由于Haussler，Littlestone和Warmestouth（1994）而引起的经典单包式图。最后，作为副产品，我们确定了一个定性和定量表征哪些类别的预测因子$ \ mathcal {h} $的维度。由于Montasser等人，这解决了一个空旷的问题。 （2019年），并在固定稳健学习的样品复杂性上，在已建立的上限和下限之间结束了一个（潜在的）无限差距。
We present a minimax optimal learner for the problem of learning predictors robust to adversarial examples at test-time. Interestingly, we find that this requires new algorithmic ideas and approaches to adversarially robust learning. In particular, we show, in a strong negative sense, the suboptimality of the robust learner proposed by Montasser, Hanneke, and Srebro (2019) and a broader family of learners we identify as local learners. Our results are enabled by adopting a global perspective, specifically, through a key technical contribution: the global one-inclusion graph, which may be of independent interest, that generalizes the classical one-inclusion graph due to Haussler, Littlestone, and Warmuth (1994). Finally, as a byproduct, we identify a dimension characterizing qualitatively and quantitatively what classes of predictors $\mathcal{H}$ are robustly learnable. This resolves an open problem due to Montasser et al. (2019), and closes a (potentially) infinite gap between the established upper and lower bounds on the sample complexity of adversarially robust learning.
