  Fairness-aware learning is a novel framework for classification tasks. Like
regular empirical risk minimization (ERM), it aims to learn a classifier with a
low error rate, and at the same time, for the predictions of the classifier to
be independent of sensitive features, such as gender, religion, race, and
ethnicity. Existing methods can achieve low dependencies on given samples, but
this is not guaranteed on unseen samples. The existing fairness-aware learning
algorithms employ different dependency measures, and each algorithm is
specifically designed for a particular one. Such diversity makes it difficult
to theoretically analyze and compare them. In this paper, we propose a general
framework for fairness-aware learning that uses f-divergences and that covers
most of the dependency measures employed in the existing methods. We introduce
a way to estimate the f-divergences that allows us to give a unified analysis
for the upper bound of the estimation error; this bound is tighter than that of
the existing convergence rate analysis of the divergence estimation. With our
divergence estimate, we propose a fairness-aware learning algorithm, and
perform a theoretical analysis of its generalization error. Our analysis
reveals that, under mild assumptions and even with enforcement of fairness, the
generalization error of our method is $O(\sqrt{1/n})$, which is the same as
that of the regular ERM. In addition, and more importantly, we show that, for
any f-divergence, the upper bound of the estimation error of the divergence is
$O(\sqrt{1/n})$. This indicates that our fairness-aware learning algorithm
guarantees low dependencies on unseen samples for any dependency measure
represented by an f-divergence.
