Removing Disparate Impact on Model Accuracy in Differentially Private Stochastic Gradient Descent

In differentially private stochastic gradient descent (DPSGD), gradient clipping and random noise addition disproportionately affect underrepresented and complex classes and subgroups. As a consequence, DPSGD has disparate impact: the accuracy of a model trained using DPSGD tends to decrease more on these classes and subgroups vs. the original, non-private model. If the original model is unfair in the sense that its accuracy is not the same across all subgroups, DPSGD exacerbates this unfairness. In this work, we study the inequality in utility loss due to differential privacy, which compares the changes in prediction accuracy w.r.t. each group between the private model and the non-private model. We analyze the cost of privacy w.r.t. each group and explain how the group sample size along with other factors is related to the privacy impact on group accuracy. Furthermore, we propose a modified DPSGD algorithm, called DPSGD-F, to achieve differential privacy, equal costs of differential privacy, and good utility. DPSGD-F adaptively adjusts the contribution of samples in a group depending on the group clipping bias such that differential privacy has no disparate impact on group accuracy. Our experimental evaluation shows the effectiveness of our removal algorithm on achieving equal costs of differential privacy with satisfactory utility.