English
Related papers

Related papers: Stochastic quasi-Newton with line-search regulariz…

200 papers

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…

Optimization and Control · Mathematics 2014-12-05 Xiao Wang , Shiqian Ma , Wei Liu

Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to…

Numerical Analysis · Computer Science 2012-06-22 Philipp Hennig , Martin Kiefel

We present a quasi-Newton method for unconstrained stochastic optimization. Most existing literature on this topic assumes a setting of stochastic optimization in which a finite sum of component functions is a reasonable approximation of an…

Optimization and Control · Mathematics 2024-09-04 Matt Menickelly , Stefan M. Wild , Miaolan Xie

We consider stochastic zero-order optimization problems, which arise in settings from simulation optimization to reinforcement learning. We propose an adaptive sampling quasi-Newton method where we estimate the gradients of a stochastic…

Optimization and Control · Mathematics 2019-10-31 Raghu Bollapragada , Stefan M. Wild

We consider unconstrained stochastic optimization problems with no available gradient information. Such problems arise in settings from derivative-free simulation optimization to reinforcement learning. We propose an adaptive sampling…

Optimization and Control · Mathematics 2021-09-28 Raghu Bollapragada , Stefan M. Wild

Second-order methods are emerging as promising alternatives to standard first-order optimizers such as gradient descent and ADAM for training neural networks. Though the advantages of including curvature information in computing…

Machine Learning · Computer Science 2025-10-15 Conor Rowan

Optimization problems, arise in many practical applications, from the view points of both theory and numerical methods. Especially, significant improvement in deep learning training came from the Quasi-Newton methods. Quasi-Newton search…

Optimization and Control · Mathematics 2024-11-19 Jiongcheng Li

Quasi-Newton algorithms are among the most popular iterative methods for solving unconstrained minimization problems, largely due to their favorable superlinear convergence property. However, existing results for these algorithms are…

Optimization and Control · Mathematics 2023-07-26 Ruichen Jiang , Qiujiang Jin , Aryan Mokhtari

We present an algorithm for minimizing a sum of functions that combines the computational efficiency of stochastic gradient descent (SGD) with the second order curvature information leveraged by quasi-Newton methods. We unify these…

Machine Learning · Computer Science 2014-12-02 Jascha Sohl-Dickstein , Ben Poole , Surya Ganguli

Training in supervised deep learning is computationally demanding, and the convergence behavior is usually not fully understood. We introduce and study a second-order stochastic quasi-Gauss-Newton (SQGN) optimization method that combines…

Machine Learning · Computer Science 2020-07-02 Christopher Thiele , Mauricio Araya-Polo , Detlef Hohl

Classical convergence analyses for optimization algorithms rely on the widely-adopted uniform smoothness assumption. However, recent experimental studies have demonstrated that many machine learning problems exhibit non-uniform smoothness,…

Machine Learning · Computer Science 2024-09-27 Zhenyu Sun , Ermin Wei

Many practical optimization problems involve objective function values that are corrupted by unavoidable numerical errors. In smooth nonconvex optimization, quasi-Newton methods combined with line search are widely used due to their…

Optimization and Control · Mathematics 2026-03-12 Hiroki Hamaguchi , Naoki Marumo , Akiko Takeda

In recent years, various subspace algorithms have been developed to handle large-scale optimization problems. Although existing subspace Newton methods require fewer iterations to converge in practice, the matrix operations and full…

Optimization and Control · Mathematics 2024-06-05 Taisei Miyaishi , Ryota Nozawa , Pierre-Louis Poirion , Akiko Takeda

The main focus in this paper is exact linesearch methods for minimizing a quadratic function whose Hessian is positive definite. We give a class of limited-memory quasi-Newton Hessian approximations which generate search directions parallel…

Optimization and Control · Mathematics 2023-05-04 David Ek , Anders Forsgren

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We…

Optimization and Control · Mathematics 2017-05-23 Xiao Wang , Shiqian Ma , Donald Goldfarb , Wei Liu

This paper presents a model-free approximation for the Hessian of the performance of deterministic policies to use in the context of Reinforcement Learning based on Quasi-Newton steps in the policy parameters. We show that the approximate…

Machine Learning · Computer Science 2022-03-29 Arash Bahari Kordabad , Hossein Nejatbakhsh Esfahani , Wenqi Cai , Sebastien Gros

Stochastic optimization methods have become a class of popular optimization tools in machine learning. Especially, stochastic gradient descent (SGD) has been widely used for machine learning problems such as training neural networks due to…

Optimization and Control · Mathematics 2021-02-26 Qingsong Zhang , Feihu Huang , Cheng Deng , Heng Huang

Two classes of methods have been proposed for escaping from saddle points with one using the second-order information carried by the Hessian and the other adding the noise into the first-order information. The existing analysis for…

Optimization and Control · Mathematics 2018-03-05 Yi Xu , Rong Jin , Tianbao Yang

This paper proposes a nonmonotone proximal quasi-Newton algorithm for unconstrained convex multiobjective composite optimization problems. To design the search direction, we minimize the max-scalarization of the variations of the Hessian…

Optimization and Control · Mathematics 2023-10-04 Xiaoxue Jiang

We propose a second-order (Hessian or Hessian-free) based optimization method for variational inference inspired by Gaussian backpropagation, and argue that quasi-Newton optimization can be developed as well. This is accomplished by…

Machine Learning · Statistics 2017-03-30 Kai Fan , Ziteng Wang , Jeff Beck , James Kwok , Katherine Heller