We theoretically study the impact of differential privacy on fairness in classification. We prove that, given a class of models, popular group fairness measures are pointwise Lipschitz-continuous with respect to the parameters of the model. This result is a consequence of a more general statement on accuracy conditioned on an arbitrary event (such as membership to a sensitive group), which may be of independent interest. We use this Lipschitz property to prove a non-asymptotic bound showing that, as the number of samples increases, the fairness level of private models gets closer to the one of their non-private counterparts. This bound also highlights the importance of the confidence margin of a model on the disparate impact of differential privacy.
@article{arxiv.2210.16242,
title = {Differential Privacy has Bounded Impact on Fairness in Classification},
author = {Paul Mangold and Michaël Perrot and Aurélien Bellet and Marc Tommasi},
journal= {arXiv preprint arXiv:2210.16242},
year = {2023}
}