Differential private optimization for nonconvex smooth objective is considered. In the previous work, the best known utility bound is O(√(d)/(nε_DP)) in terms of the squared full gradient norm, which is achieved by Differential Private Gradient Descent (DP-GD) as an instance, where n is the sample size, d is the problem dimensionality and ε_DP is the differential privacy parameter. To improve the best known utility bound, we propose a new differential private optimization framework called DIFF2…