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In this paper, we propose Nesterov Accelerated Shuffling Gradient (NASG), a new algorithm for the convex finite-sum minimization problems. Our method integrates the traditional Nesterov's acceleration momentum with different shuffling…

Optimization and Control · Mathematics 2022-06-14 Trang H. Tran , Katya Scheinberg , Lam M. Nguyen

Stochastic optimization is a cornerstone of modern machine learning. This paper studies the generalization performance of two classical stochastic optimization algorithms: stochastic gradient descent (SGD) and Nesterov's accelerated…

Machine Learning · Computer Science 2026-03-20 Shaojie Li , Pengwei Tang , Yong Liu

We combine two advanced ideas widely used in optimization for machine learning: shuffling strategy and momentum technique to develop a novel shuffling gradient-based method with momentum, coined Shuffling Momentum Gradient (SMG), for…

Optimization and Control · Mathematics 2021-06-10 Trang H. Tran , Lam M. Nguyen , Quoc Tran-Dinh

We prove that various stochastic gradient descent methods, including the stochastic gradient descent (SGD), stochastic heavy-ball (SHB), and stochastic Nesterov's accelerated gradient (SNAG) methods, almost surely avoid any strict saddle…

Machine Learning · Computer Science 2023-02-16 Jun Liu , Ye Yuan

Stochastic gradient descent (\textsc{Sgd}) methods are the most powerful optimization tools in training machine learning and deep learning models. Moreover, acceleration (a.k.a. momentum) methods and diagonal scaling (a.k.a. adaptive…

Machine Learning · Statistics 2018-10-02 Qi Deng , Yi Cheng , Guanghui Lan

The optimization step in many machine learning problems rarely relies on vanilla gradient descent but it is common practice to use momentum-based accelerated methods. Despite these algorithms being widely applied to arbitrary loss…

Disordered Systems and Neural Networks · Physics 2021-10-29 Stefano Sarao Mannelli , Pierfrancesco Urbani

In this paper, we provide a comprehensive theoretical analysis of Stochastic Gradient Descent (SGD) and its momentum variants (Polyak Heavy-Ball and Nesterov) for tracking time-varying optima under strong convexity and smoothness. Our…

Machine Learning · Statistics 2026-05-20 Sharan Sahu , Cameron J. Hogan , Martin T. Wells

Stochastic gradient descent with momentum (SGDM) methods have become fundamental optimization tools in machine learning, combining the computational efficiency of stochastic gradients with the acceleration benefits of momentum. Despite…

Optimization and Control · Mathematics 2026-03-02 Zimeng Wang , Alp Yurtsever

Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the…

Machine Learning · Computer Science 2021-06-08 Jun-Kun Wang , Chi-Heng Lin , Jacob Abernethy

Gradient descent-based optimization methods underpin the parameter training of neural networks, and hence comprise a significant component in the impressive test results found in a number of applications. Introducing stochasticity is key to…

Machine Learning · Computer Science 2021-06-01 Nikola B. Kovachki , Andrew M. Stuart

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

We study stochastic second-order methods for solving general non-convex optimization problems. We propose using a special version of momentum to stabilize the stochastic gradient and Hessian estimates in Newton's method. We show that…

Optimization and Control · Mathematics 2025-06-27 El Mahdi Chayti , Nikita Doikov , Martin Jaggi

This paper proposes an accelerated proximal stochastic variance reduced gradient (ASVRG) method, in which we design a simple and effective momentum acceleration trick. Unlike most existing accelerated stochastic variance reduction methods…

Machine Learning · Computer Science 2018-11-20 Fanhua Shang , Licheng Jiao , Kaiwen Zhou , James Cheng , Yan Ren , Yufei Jin

Simple stochastic momentum methods are widely used in machine learning optimization, but their good practical performance is at odds with an absence of theoretical guarantees of acceleration in the literature. In this work, we aim to close…

Machine Learning · Computer Science 2025-06-24 Raghu Bollapragada , Tyler Chen , Rachel Ward

We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them. SVRG and related methods have recently surged into prominence for convex optimization given their edge over stochastic gradient…

Optimization and Control · Mathematics 2016-04-06 Sashank J. Reddi , Ahmed Hefny , Suvrit Sra , Barnabas Poczos , Alex Smola

Machine learning and deep learning are widely researched fields that provide solutions to many modern problems. Due to the complexity of new problems related to the size of datasets, efficient approaches are obligatory. In optimization…

Optimization and Control · Mathematics 2025-10-01 Stepan Trifonov , Leonid Levin , Savelii Chezhegov , Aleksandr Beznosikov

Due to its simplicity and outstanding ability to generalize, stochastic gradient descent (SGD) is still the most widely used optimization method despite its slow convergence. Meanwhile, adaptive methods have attracted rising attention of…

Optimization and Control · Mathematics 2020-06-15 Xunpeng Huang , Runxin Xu , Hao Zhou , Zhe Wang , Zhengyang Liu , Lei Li

We study stochastic gradient descent (SGD) and the stochastic heavy ball method (SHB, otherwise known as the momentum method) for the general stochastic approximation problem. For SGD, in the convex and smooth setting, we provide the first…

Machine Learning · Computer Science 2021-02-08 Othmane Sebbouh , Robert M. Gower , Aaron Defazio

Stochastic optimization algorithms, particularly stochastic policy gradient (SPG), report significant success in reinforcement learning (RL). Nevertheless, up to now, that how to speedily acquire an optimal solution for RL is still a…

Machine Learning · Computer Science 2024-05-22 Haobin Zhang , Zhuang Yang

Polyak's Heavy Ball (PHB; Polyak, 1964), a.k.a. Classical Momentum, and Nesterov's Accelerated Gradient (NAG; Nesterov, 1983) are well-established momentum-descent methods for optimization. Although the latter generally outperforms the…

Optimization and Control · Mathematics 2025-08-01 Cédric M. Campos , David Martín de Diego , José Torrente