  Recent works have shown that selecting an optimal model architecture suited
to the differential privacy setting is necessary to achieve the best possible
utility for a given privacy budget using differentially private stochastic
gradient descent (DP-SGD)(Tramer and Boneh 2020; Cheng et al. 2022). In light
of these findings, we empirically analyse how different fairness notions,
belonging to distinct classes of statistical fairness criteria (independence,
separation and sufficiency), are impacted when one selects a model architecture
suitable for DP-SGD, optimized for utility. Using standard datasets from ML
fairness literature, we show using a rigorous experimental protocol, that by
selecting the optimal model architecture for DP-SGD, the differences across
groups concerning the relevant fairness metrics (demographic parity, equalized
odds and predictive parity) more often decrease or are negligibly impacted,
compared to the non-private baseline, for which optimal model architecture has
also been selected to maximize utility. These findings challenge the
understanding that differential privacy will necessarily exacerbate unfairness
in deep learning models trained on biased datasets.
