  The performance cost of differential privacy has, for some applications, been
shown to be higher for minority groups; fairness, conversely, has been shown to
disproportionally compromise the privacy of members of such groups. Most work
in this area has been restricted to computer vision and risk assessment. In
this paper, we evaluate the impact of differential privacy on fairness across
four tasks, focusing on how attempts to mitigate privacy violations and
between-group performance differences interact: Does privacy inhibit attempts
to ensure fairness? To this end, we train $(\varepsilon,\delta)$-differentially
private models with empirical risk minimization and group distributionally
robust training objectives. Consistent with previous findings, we find that
differential privacy increases between-group performance differences in the
baseline setting; but more interestingly, differential privacy reduces
between-group performance differences in the robust setting. We explain this by
reinterpreting differential privacy as regularization.
