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We study the problem of \emph{adversarially robust} PAC learning. In this framework, the learner observes independent samples from an unknown distribution over $\mathcal{X} \times \{0,1\}$, as in classical PAC learning. However, given a perturbation map $\mathcal{U} : \mathcal{X} \to 2^{\mathcal{X}}$ known to the learn...
This work introduces a novel combinatorial dimension of the reward class which is called the alignment dimension, and shows that it completely characterizes the alignment learnability --- a reward class is alignment learnable if and only if its alignment dimension is finite.
This work improves the upper bound to match the best known lower bound, thus establishing the optimal error guarantee for learning under Tsybakov noise.
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