  In this paper, we take a first step towards answering the question of how to
design fair machine learning algorithms that are robust to adversarial attacks.
Using a minimax framework, we aim to design an adversarially robust fair
regression model that achieves optimal performance in the presence of an
attacker who is able to add a carefully designed adversarial data point to the
dataset or perform a rank-one attack on the dataset. By solving the proposed
nonsmooth nonconvex-nonconcave minimax problem, the optimal adversary as well
as the robust fairness-aware regression model are obtained. For both synthetic
data and real-world datasets, numerical results illustrate that the proposed
adversarially robust fair models have better performance on poisoned datasets
than other fair machine learning models in both prediction accuracy and
group-based fairness measure.
