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math.OC2019★ 18 cited
Sharp Analysis for Nonconvex SGD Escaping from Saddle Points
Cong Fang, Zhouchen Lin, Tong Zhang
In this paper, we give a sharp analysis for Stochastic Gradient Descent (SGD) and prove that SGD is able to efficiently escape from saddle points and find an -appr…
math.OC2017★ 20 cited
Second-Order Methods with Cubic Regularization Under Inexact Information
Saeed Ghadimi, Han Liu, Tong Zhang
In this paper, we generalize (accelerated) Newton's method with cubic regularization under inexact second-order information for (strongly) convex optimization problems. Under mild…