English
Related papers

Related papers: Shuffling Momentum Gradient Algorithm for Convex O…

200 papers

We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…

Optimization and Control · Mathematics 2022-03-24 Hailiang Liu , Xuping Tian

Stochastic gradient descent (SGD), which dates back to the 1950s, is one of the most popular and effective approaches for performing stochastic optimization. Research on SGD resurged recently in machine learning for optimizing convex loss…

Machine Learning · Computer Science 2019-12-24 Jie Chen , Ronny Luss

Large-scale constrained optimization problems are at the core of many tasks in control, signal processing, and machine learning. Notably, problems with functional constraints arise when, beyond a performance{\nobreakdash-}centric goal…

Optimization and Control · Mathematics 2025-05-15 Antesh Upadhyay , Sang Bin Moon , Abolfazl Hashemi

Stochastic optimization lies at the heart of machine learning, and its cornerstone is stochastic gradient descent (SGD), a method introduced over 60 years ago. The last 8 years have seen an exciting new development: variance reduction (VR)…

Machine Learning · Computer Science 2020-10-05 Robert M. Gower , Mark Schmidt , Francis Bach , Peter Richtarik

Stochastic gradient descent~(SGD) and its variants have been the dominating optimization methods in machine learning. Compared to SGD with small-batch training, SGD with large-batch training can better utilize the computational power of…

Machine Learning · Statistics 2024-04-16 Shen-Yi Zhao , Chang-Wei Shi , Yin-Peng Xie , Wu-Jun Li

Stochastic gradient methods (SGMs) have been extensively used for solving stochastic problems or large-scale machine learning problems. Recent works employ various techniques to improve the convergence rate of SGMs for both convex and…

Optimization and Control · Mathematics 2022-05-02 Yangyang Xu , Yibo Xu

We study the performance of stochastic gradient descent (SGD) on smooth and strongly-convex finite-sum optimization problems. In contrast to the majority of existing theoretical works, which assume that individual functions are sampled with…

Machine Learning · Computer Science 2021-06-03 Itay Safran , Ohad Shamir

Stochastic gradient descent with momentum (SGDM) is one of the most widely used optimization algorithms in machine learning. While optimization properties of SGDM have been extensively studied in the literature, it remains insufficiently…

Machine Learning · Computer Science 2026-05-28 Yunwen Lei , Zimeng Wang , Xiaoming Yuan

We study finite-sum nonconvex optimization problems, where the objective function is an average of $n$ nonconvex functions. We propose a new stochastic gradient descent algorithm based on nested variance reduction. Compared with…

Machine Learning · Computer Science 2020-10-20 Dongruo Zhou , Pan Xu , Quanquan Gu

Large-scale nonconvex optimization problems are ubiquitous in modern machine learning, and among practitioners interested in solving them, Stochastic Gradient Descent (SGD) reigns supreme. We revisit the analysis of SGD in the nonconvex…

Optimization and Control · Mathematics 2020-07-27 Ahmed Khaled , Peter Richtárik

Recently, Stochastic Gradient Descent (SGD) and its variants have become the dominant methods in the large-scale optimization of machine learning (ML) problems. A variety of strategies have been proposed for tuning the step sizes, ranging…

Machine Learning · Computer Science 2022-08-02 Xiaoyu Li

Momentum based stochastic gradient methods such as heavy ball (HB) and Nesterov's accelerated gradient descent (NAG) method are widely used in practice for training deep networks and other supervised learning models, as they often provide…

Machine Learning · Computer Science 2018-08-02 Rahul Kidambi , Praneeth Netrapalli , Prateek Jain , Sham M. Kakade

Stochastic gradient descent (SGD) is perhaps the most prevalent optimization method in modern machine learning. Contrary to the empirical practice of sampling from the datasets without replacement and with (possible) reshuffling at each…

Optimization and Control · Mathematics 2024-02-08 Xufeng Cai , Cheuk Yin Lin , Jelena Diakonikolas

Recently, {\it stochastic momentum} methods have been widely adopted in training deep neural networks. However, their convergence analysis is still underexplored at the moment, in particular for non-convex optimization. This paper fills the…

Optimization and Control · Mathematics 2016-05-06 Tianbao Yang , Qihang Lin , Zhe Li

When using stochastic gradient descent to solve large-scale machine learning problems, a common practice of data processing is to shuffle the training data, partition the data across multiple machines if needed, and then perform several…

Machine Learning · Statistics 2017-10-02 Qi Meng , Wei Chen , Yue Wang , Zhi-Ming Ma , Tie-Yan Liu

The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become…

Optimization and Control · Mathematics 2024-11-06 Kexin Jin , Jonas Latz , Chenguang Liu , Alessandro Scagliotti

Momentum plays a crucial role in stochastic gradient-based optimization algorithms for accelerating or improving training deep neural networks (DNNs). In deep learning practice, the momentum is usually weighted by a well-calibrated…

Machine Learning · Computer Science 2020-12-04 Bao Wang , Qiang Ye

In this paper, we study the performance of a large family of SGD variants in the smooth nonconvex regime. To this end, we propose a generic and flexible assumption capable of accurate modeling of the second moment of the stochastic…

Optimization and Control · Mathematics 2020-06-15 Zhize Li , Peter Richtárik

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

Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…

Machine Learning · Statistics 2014-11-17 Mengdi Wang , Ethan X. Fang , Han Liu