Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization
Abstract
In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that only stochastic information of the gradients of the objective function is available via a stochastic first-order oracle (SFO). Firstly, we propose a general framework of stochastic quasi-Newton methods for solving nonconvex stochastic optimization. The proposed framework extends the classic quasi-Newton methods working in deterministic settings to stochastic settings, and we prove its almost sure convergence to stationary points. Secondly, we propose a general framework for a class of randomized stochastic quasi-Newton methods, in which the number of iterations conducted by the algorithm is a random variable. The worst-case SFO-calls complexities of this class of methods are analyzed. Thirdly, we present two specific methods that fall into this framework, namely stochastic damped-BFGS method and stochastic cyclic Barzilai-Borwein method. Finally, we report numerical results to demonstrate the efficiency of the proposed methods.
Cite
@article{arxiv.1412.1196,
title = {Stochastic Quasi-Newton Methods for Nonconvex Stochastic Optimization},
author = {Xiao Wang and Shiqian Ma and Wei Liu},
journal= {arXiv preprint arXiv:1412.1196},
year = {2014}
}