Differentially Private Empirical Risk Minimization Revisited: Faster and More General

In this paper we study the differentially private Empirical Risk Minimization(ERM) problem in different settings. For smooth (strongly) convex loss function or without (non)-smooth regularization, we give algorithms that achieve optimal or near optimal utility bounds with less gradient complexity with previous work. For ERM with smooth convex loss function in-dimensional (p\ n) setting, we give an algorithm which achieves the bound with less gradient complexity than previous ones. At last, we the expected excess empirical risk from convex loss functions to-convex ones satisfying the Polyak-Lojasiewicz condition and give a tighter bound on the utility than the one in \{ijcai2017-548}.