  Data augmentation by incorporating cheap unlabeled data from multiple domains
is a powerful way to improve prediction especially when there is limited
labeled data. In this work, we investigate how adversarial robustness can be
enhanced by leveraging out-of-domain unlabeled data. We demonstrate that for
broad classes of distributions and classifiers, there exists a sample
complexity gap between standard and robust classification. We quantify to what
degree this gap can be bridged via leveraging unlabeled samples from a shifted
domain by providing both upper and lower bounds. Moreover, we show settings
where we achieve better adversarial robustness when the unlabeled data come
from a shifted domain rather than the same domain as the labeled data. We also
investigate how to leverage out-of-domain data when some structural
information, such as sparsity, is shared between labeled and unlabeled domains.
Experimentally, we augment two object recognition datasets (CIFAR-10 and SVHN)
with easy to obtain and unlabeled out-of-domain data and demonstrate
substantial improvement in the model's robustness against $\ell_\infty$
adversarial attacks on the original domain.
