A Stochastic Trust Region Method for Non-convex Minimization

Solving the trust-region subproblem using the lanczos method

Nicholas IM Gould, Stefano Lucidi, Massimo Roma, and Philippe L Toint · 1999

Earlier work this paper cites.

Trust region methods , volume 1

Andrew R Conn, Nicholas IM Gould, and Ph L Toint · 2000

Earlier work this paper cites.

Cubic regularization of newton method and its global performance

Yurii Nesterov and Boris T Polyak · 2006

Earlier work this paper cites.

Adaptive cubic regularisation methods for unconstrained optimization. part i: motivation, convergence and numerical results

Coralia Cartis, Nicholas IM Gould, and Philippe L Toint · 2011

Earlier work this paper cites.

User-friendly tail bounds for sums of random matrices

Joel A Tropp · 2012

Earlier work this paper cites.

Accelerating stochastic gradient descent using predictive variance reduction

Rie Johnson and Tong Zhang · 2013

Cited alongside, same era.

Identifying and attacking the saddle point problem in high-dimensional non-convex optimization

Yann N Dauphin, Razvan Pascanu, Caglar Gulcehre, Kyunghyun Cho, Surya Ganguli, and Yoshua Bengio · 2014

Cited alongside, same era.

Lower bounds for finding stationary points i

Original

Yair Carmon, John C Duchi, Oliver Hinder, and Aaron Sidford · 2017

Cited alongside, same era.

A trust region algorithm with a worst-case iteration complexity of (epsilon 3/2) for nonconvex optimization

Frank E Curtis, Daniel P Robinson, and Mohammadreza Samadi · 2017

Cited alongside, same era.

Sarah: A novel method for machine learning problems using stochastic recursive gradient

Lam M Nguyen, Jie Liu, Katya Scheinberg, and Martin Takáč · 2017

Cited alongside, same era.

Sub-sampled cubic regularization for non-convex optimization

Original

Jonas Moritz Kohler and Aurelien Lucchi

Cited in the paper.

Sub-sampled cubic regularization for non-convex optimization

Jonas Moritz Kohler and Aurelien Lucchi

Cited in the paper.

Stochastic variance-reduced cubic regularized Newton methods

Dongruo Zhou, Pan Xu, and Quanquan Gu

Cited in the paper.

Sample efficient stochastic variance-reduced cubic regularization method

Original

Dongruo Zhou, Pan Xu, and Quanquan Gu

Cited in the paper.

Stochastic variance-reduced cubic regularized newton method

Original

Dongruo Zhou, Pan Xu, and Quanquan Gu

Cited in the paper.

Newton-type methods for non-convex optimization under inexact hessian information

Original

Peng Xu, Farbod Roosta-Khorasani, and Michael W Mahoney · 2017

Later among the works it cites.

Spider: Near-optimal non-convex optimization via stochastic path-integrated differential estimator

Cong Fang, Chris Junchi Li, Zhouchen Lin, and Tong Zhang · 2018

Later among the works it cites.

Tracking the gradients using the hessian: A new look at variance reducing stochastic methods

Robert Gower, Nicolas Le Roux, and Francis Bach · 2018

Later among the works it cites.

Adaptive stochastic variance reduction for subsampled newton method with cubic regularization

Original

Junyu Zhang, Lin Xiao, and Shuzhong Zhang · 2018

Later among the works it cites.