  Empirical risk minimization often fails to provide robustness against
adversarial attacks in test data, causing poor out-of-sample performance.
Adversarially robust optimization (ARO) has thus emerged as the de facto
standard for obtaining models that hedge against such attacks. However, while
these models are robust against adversarial attacks, they tend to suffer
severely from overfitting. To address this issue for logistic regression, we
study the Wasserstein distributionally robust (DR) counterpart of ARO and show
that this problem admits a tractable reformulation. Furthermore, we develop a
framework to reduce the conservatism of this problem by utilizing an auxiliary
dataset (e.g., synthetic, external, or out-of-domain data), whenever available,
with instances independently sampled from a nonidentical but related ground
truth. In particular, we intersect the ambiguity set of the DR problem with
another Wasserstein ambiguity set that is built using the auxiliary dataset. We
analyze the properties of the underlying optimization problem, develop
efficient solution algorithms, and demonstrate that the proposed method
consistently outperforms benchmark approaches on real-world datasets.
