A Proximal Stochastic Quasi-Newton Algorithm
In this paper, we discuss the problem of minimizing the sum of two convex functions: a smooth function plus a non-smooth function. Further, the smooth part can be expressed by the average of a large number of smooth component functions, and the non-smooth part is equipped with a simple proximal mapping. We propose a proximal stochastic second-order method, which is efficient and scalable. It incorporates the Hessian in the smooth part of the function and exploits multistage scheme to reduce the variance of the stochastic gradient. We prove that our method can achieve linear rate of convergence.
Code (0)
등록된 구현이 없습니다.
Similar Papers 제목 키워드 기반
A Stochastic Extra-Step Quasi-Newton Method for Nonsmooth Nonconvex Optimization
In this paper, a novel stochastic extra-step quasi-Newton method is developed to solve a class of nonsmooth nonconvex composite optimization problems. We assume that the gradient of the smooth part of the objective funct…
Proximal Quasi-Newton Methods for Regularized Convex Optimization with Linear and Accelerated Sublinear Convergence Rates
In [19], a general, inexact, efficient proximal quasi-Newton algorithm for composite optimization problems has been proposed and a sublinear global convergence rate has been established. In this paper, we analyze the con…
Proximal Quasi-Newton for Computationally Intensive L1-regularized M-estimators
We consider the class of optimization problems arising from computationally intensive L1-regularized M-estimators, where the function or gradient values are very expensive to compute. A particular instance of interest is…
General ClassificationStructured PredictionA Variance Reduced Stochastic Newton Method
Quasi-Newton methods are widely used in practise for convex loss minimization problems. These methods exhibit good empirical performance on a wide variety of tasks and enjoy super-linear convergence to the optimal soluti…
A Stochastic Variance Reduced Nesterov's Accelerated Quasi-Newton Method
Recently algorithms incorporating second order curvature information have become popular in training neural networks. The Nesterov's Accelerated Quasi-Newton (NAQ) method has shown to effectively accelerate the BFGS quas…
regression