Differentially Private Convex Optimization with Piecewise Affine Objectives Using Projections and Average Subgradients

Han et al. introduced an iterative, differentially private method for solving convex constrained optimization problems with piecewise affine objectives: the differentially private subgradient method. In this paper, we propose extensions to this method to guarantee solutions stay within the feasible region and introduce a hyperparameter () to allow the optimization algorithm to take an average subgradient (the differentially private average subgradient method). We find evidence that tuning and using projections can increase performance.