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Stochastic Heavy Ball (SHB) and Nesterov's Accelerated Stochastic Gradient (ASG) are popular momentum methods in stochastic optimization. While benefits of such acceleration ideas in deterministic settings are well understood, their…

Machine Learning · Computer Science 2022-07-12 Swetha Ganesh , Rohan Deb , Gugan Thoppe , Amarjit Budhiraja

Training neural networks requires optimizing a loss function that may be highly irregular, and in particular neither convex nor smooth. Popular training algorithms are based on stochastic gradient descent with momentum (SGDM), for which…

Machine Learning · Computer Science 2026-03-17 Qinzi Zhang , Ashok Cutkosky

The stochastic heavy ball momentum (SHBM) method has gained considerable popularity as a scalable approach for solving large-scale optimization problems. However, one limitation of this method is its reliance on prior knowledge of certain…

Optimization and Control · Mathematics 2024-04-04 Yun Zeng , Deren Han , Yansheng Su , Jiaxin Xie

Momentum method has been used extensively in optimizers for deep learning. Recent studies show that distributed training through K-step averaging has many nice properties. We propose a momentum method for such model averaging approaches. At…

Machine Learning · Computer Science 2021-10-05 Guojing Cong , Tianyi Liu

Stochastic gradient methods with momentum are widely used in applications and at the core of optimization subroutines in many popular machine learning libraries. However, their sample complexities have not been obtained for problems beyond…

Optimization and Control · Mathematics 2021-02-12 Vien V. Mai , Mikael Johansson

The stochastic momentum method is a commonly used acceleration technique for solving large-scale stochastic optimization problems in artificial neural networks. Current convergence results of stochastic momentum methods under non-convex…

Optimization and Control · Mathematics 2023-01-26 Dongpo Xu , Jinlan Liu , Yinghua Lu , Jun Kong , Danilo Mandic

A number of optimization approaches have been proposed for optimizing nonconvex objectives (e.g. deep learning models), such as batch gradient descent, stochastic gradient descent and stochastic variance reduced gradient descent. Theory…

Machine Learning · Computer Science 2019-05-15 Jia Bi , Steve R. Gunn

In this work, we provide a fundamental unified convergence theorem used for deriving expected and almost sure convergence results for a series of stochastic optimization methods. Our unified theorem only requires to verify several…

Optimization and Control · Mathematics 2022-10-20 Xiao Li , Andre Milzarek

In this paper, we propose a novel accelerated stochastic gradient method with momentum, which momentum is the weighted average of previous gradients. The weights decays inverse proportionally with the iteration times. Stochastic gradient…

Machine Learning · Computer Science 2020-06-02 Liang Liu , Xiaopeng Luo

Stochastic heavy ball momentum (SHB) is commonly used to train machine learning models, and often provides empirical improvements over stochastic gradient descent. By primarily focusing on strongly-convex quadratics, we aim to better…

Optimization and Control · Mathematics 2025-06-02 Anh Dang , Reza Babanezhad , Sharan Vaswani

We present a finite-time analysis of two smoothed functional stochastic approximation algorithms for simulation-based optimization. The first is a two time-scale gradient-based method, while the second is a three time-scale Newton-based…

Machine Learning · Computer Science 2026-04-01 Kaustubh Kartikey , Shalabh Bhatnagar

We consider gradient descent with `momentum', a widely used method for loss function minimization in machine learning. This method is often used with `Nesterov acceleration', meaning that the gradient is evaluated not at the current…

Machine Learning · Computer Science 2020-01-20 Goran Nakerst , John Brennan , Masudul Haque

In this work, we consider smooth unconstrained optimization problems and we deal with the class of gradient methods with momentum, i.e., descent algorithms where the search direction is defined as a linear combination of the current…

Optimization and Control · Mathematics 2025-12-04 Matteo Lapucci , Giampaolo Liuzzi , Stefano Lucidi , Davide Pucci , Marco Sciandrone

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…

Optimization and Control · Mathematics 2019-04-30 David Kozak , Stephen Becker , Alireza Doostan , Luis Tenorio

Distributed optimization advances centralized machine learning methods by enabling parallel and decentralized learning processes over a network of computing nodes. This work provides an accelerated consensus-based distributed algorithm for…

Systems and Control · Electrical Eng. & Systems 2025-07-01 Mohammadreza Doostmohammadian , Hamid R. Rabiee

Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…

Optimization and Control · Mathematics 2021-01-01 Lihua Lei , Michael I. Jordan

This paper presents a novel stochastic gradient descent algorithm for constrained optimization. The proposed algorithm randomly samples constraints and components of the finite sum objective function and relies on a relaxed logarithmic…

Optimization and Control · Mathematics 2025-05-13 Naum Dimitrieski , Jing Cao , Christian Ebenbauer

We analyze a class of stochastic gradient algorithms with momentum on a high-dimensional random least squares problem. Our framework, inspired by random matrix theory, provides an exact (deterministic) characterization for the sequence of…

Optimization and Control · Mathematics 2021-10-27 Courtney Paquette , Elliot Paquette

An algorithm is presented for momentum gradient descent optimization based on the first-order differential equation of the Newtonian dynamics. The fictitious mass is introduced to the dynamics of momentum for regularizing the adaptive…

Machine Learning · Computer Science 2018-05-15 Zhidong Han

Distributed stochastic optimization algorithms can simultaneously process large-scale datasets, significantly accelerating model training. However, their effectiveness is often hindered by the sparsity of distributed networks and data…

Machine Learning · Computer Science 2025-02-14 Yuchen Hu , Xi Chen , Weidong Liu , Xiaojun Mao