  We initiate the study of fair classifiers that are robust to perturbations in
the training distribution. Despite recent progress, the literature on fairness
has largely ignored the design of fair and robust classifiers. In this work, we
develop classifiers that are fair not only with respect to the training
distribution, but also for a class of distributions that are weighted
perturbations of the training samples. We formulate a min-max objective
function whose goal is to minimize a distributionally robust training loss, and
at the same time, find a classifier that is fair with respect to a class of
distributions. We first reduce this problem to finding a fair classifier that
is robust with respect to the class of distributions. Based on online learning
algorithm, we develop an iterative algorithm that provably converges to such a
fair and robust solution. Experiments on standard machine learning fairness
datasets suggest that, compared to the state-of-the-art fair classifiers, our
classifier retains fairness guarantees and test accuracy for a large class of
perturbations on the test set. Furthermore, our experiments show that there is
an inherent trade-off between fairness robustness and accuracy of such
classifiers.
