Differentially Private Optimization for Smooth Nonconvex ERM

Changyu Gao, Stephen J. Wright

Abstract: We develop simple differentially private optimization algorithms that move along directions of (expected) descent to find an approximate second-order solution for nonconvex ERM. We use line search, mini-batching, and a two-phase strategy to improve the speed and practicality of the algorithm. Numerical experiments demonstrate the effectiveness of these approaches.