Recently, Montasser et al. [2019] showed that finite VC dimension is not sufficient for proper adversarially robust PAC learning. In light of this hardness, there is a growing effort to study what type of relaxations to the adversarially robust PAC learning setup can enable proper learnability. In this work, we initiate the study of proper learning under relaxations of the worst-case robust loss. We give a family of robust loss relaxations under which VC classes are properly PAC learnable with sample complexity close to what one would require in the standard PAC learning setup. On the other hand, we show that for an existing and natural relaxation of the worst-case robust loss, finite VC dimension is not sufficient for proper learning. Lastly, we give new generalization guarantees for the adversarially robust empirical risk minimizer.

翻译：近期，Montasser等人[2019]的研究表明，有限的VC维不足以支撑对抗鲁棒PAC学习框架下的恰当学习。针对这一困难，学界正积极探索何种类型的对抗鲁棒PAC学习框架的松弛机制能够实现恰当可学习性。本文首次系统研究最坏情形鲁棒损失函数松弛条件下的恰当学习问题。我们提出了一族鲁棒损失松弛函数，在该松弛框架下VC类能够以接近标准PAC学习所需样本复杂度实现恰当PAC可学习。另一方面，研究表明对于既有的一种自然的最坏情形鲁棒损失松弛函数，有限的VC维仍不足以实现恰当学习。最后，我们给出了对抗鲁棒经验风险最小化器的新颖泛化保证。