Efficient Private ERM for Smooth Objectives

Efficient Private ERM for Smooth Objectives

Jiaqi Zhang, Kai Zheng, Wenlong Mou, Liwei Wang

Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence
Main track. Pages 3922-3928. https://doi.org/10.24963/ijcai.2017/548

In this paper, we consider efficient differentially private empirical risk minimization from the viewpoint of optimization algorithms. For strongly convex and smooth objectives, we prove that gradient descent with output perturbation not only achieves nearly optimal utility, but also significantly improves the running time of previous state-of-the-art private optimization algorithms, for both $\epsilon$-DP and $(\epsilon, \delta)$-DP. For non-convex but smooth objectives, we propose an RRPSGD (Random Round Private Stochastic Gradient Descent) algorithm, which provably converges to a stationary point with privacy guarantee. Besides the expected utility bounds, we also provide guarantees in high probability form. Experiments demonstrate that our algorithm consistently outperforms existing method in both utility and running time.
Keywords:
Multidisciplinary Topics and Applications: AI&Security and Privacy
Machine Learning: Machine Learning