Li Zhang, Doctor, Academy of Mathematics and Systems Science, Chinese Academy of Sciences

Cubic Regularization Method for Distributed Nonconvex Optimization via Gradient Tracking

16:00-17:00 September 20 (Wednesday), Z311

The problem of saddle-point avoidance in distributed nonconvex optimization is extraordinarily challenging in large-scale frameworks, such as power systems and deep neural networks. The cubic regularization method is introduced for effectively escaping saddle points in centralized optimization. We further explore the cubic regularization method in distributed framework and take the method of tracking to restructure an algorithm in order to overcome the obstacles from saddle-point avoidance. With the absence of similarity conditions, the iteration complexity of the designed algorithm is found at the order Ο(ε−1.5) with accuracyε under Lipschitz conditions of Hessian functions, which is the same with centralized optimization and is much lower than related works with  Ο(ε-2).