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In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…

Machine Learning · Computer Science 2022-10-11 Vivak Patel , Shushu Zhang , Bowen Tian

Stochastic gradient descent (SGD) is a widely used algorithm in machine learning, particularly for neural network training. Recent studies on SGD for canonical quadratic optimization or linear regression show it attains well generalization…

Machine Learning · Computer Science 2024-09-17 Haihan Zhang , Yuanshi Liu , Qianwen Chen , Cong Fang

Recent works have shown that high probability metrics with stochastic gradient descent (SGD) exhibit informativeness and in some cases advantage over the commonly adopted mean-square error-based ones. In this work we provide a formal…

Machine Learning · Computer Science 2022-11-03 Dragana Bajovic , Dusan Jakovetic , Soummya Kar

Stochastic Gradient Descent (SGD) is widely used in machine learning research. Previous convergence analyses of SGD under the vanishing step-size setting typically require Robbins-Monro conditions. However, in practice, a wider variety of…

Machine Learning · Computer Science 2025-04-18 Ruinan Jin , Difei Cheng , Hong Qiao , Xin Shi , Shaodong Liu , Bo Zhang

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

Optimization and Control · Mathematics 2025-02-25 Chenhao Yu , Yusu Hong , Junhong Lin

The classical analysis of Stochastic Gradient Descent (SGD) with polynomially decaying stepsize $\eta_t = \eta/\sqrt{t}$ relies on well-tuned $\eta$ depending on problem parameters such as Lipschitz smoothness constant, which is often…

Optimization and Control · Mathematics 2023-05-23 Junchi Yang , Xiang Li , Ilyas Fatkhullin , Niao He

The dynamical stability of optimization methods at the vicinity of minima of the loss has recently attracted significant attention. For gradient descent (GD), stable convergence is possible only to minima that are sufficiently flat w.r.t.…

Machine Learning · Computer Science 2024-06-18 Rotem Mulayoff , Tomer Michaeli

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 consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

Machine Learning · Statistics 2018-12-27 Lam M. Nguyen , Nam H. Nguyen , Dzung T. Phan , Jayant R. Kalagnanam , Katya Scheinberg

We study the asynchronous stochastic gradient descent algorithm for distributed training over $n$ workers which have varying computation and communication frequency over time. In this algorithm, workers compute stochastic gradients in…

Machine Learning · Computer Science 2022-06-17 Anastasia Koloskova , Sebastian U. Stich , Martin Jaggi

Stochastic Gradient Descent (SGD) plays a central role in modern machine learning. While there is extensive work on providing error upper bound for SGD, not much is known about SGD error lower bound. In this paper, we study the convergence…

Optimization and Control · Mathematics 2019-10-21 Zhiyan Ding , Yiding Chen , Qin Li , Xiaojin Zhu

Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…

Machine Learning · Computer Science 2024-02-13 Anuraganand Sharma

Motivated by broad applications in reinforcement learning and machine learning, this paper considers the popular stochastic gradient descent (SGD) when the gradients of the underlying objective function are sampled from Markov processes.…

Optimization and Control · Mathematics 2020-04-02 Thinh T. Doan , Lam M. Nguyen , Nhan H. Pham , Justin Romberg

In the past several years, the last-iterate convergence of the Stochastic Gradient Descent (SGD) algorithm has triggered people's interest due to its good performance in practice but lack of theoretical understanding. For Lipschitz convex…

Machine Learning · Computer Science 2026-03-20 Zijian Liu , Zhengyuan Zhou

We study to what extent may stochastic gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit to training data. We consider the fundamental stochastic convex…

Machine Learning · Computer Science 2023-01-13 Tomer Koren , Roi Livni , Yishay Mansour , Uri Sherman

We study stochastic gradient descent (SGD) with gradient clipping on convex functions under a generalized smoothness assumption called $(L_0,L_1)$-smoothness. Using gradient clipping, we establish a high probability convergence rate that…

Optimization and Control · Mathematics 2025-06-04 Ofir Gaash , Kfir Yehuda Levy , Yair Carmon

Distributed stochastic gradient descent (SGD) has attracted considerable recent attention due to its potential for scaling computational resources, reducing training time, and helping protect user privacy in machine learning. However, the…

Machine Learning · Computer Science 2025-02-27 Siyuan Yu , Wei Chen , H. Vincent Poor

We consider a class of stochastic smooth convex optimization problems under rather general assumptions on the noise in the stochastic gradient observation. As opposed to the classical problem setting in which the variance of noise is…

Optimization and Control · Mathematics 2024-08-23 Sasila Ilandarideva , Anatoli Juditsky , Guanghui Lan , Tianjiao Li

We consider stochastic convex optimization problems where the objective is an expectation over smooth functions. For this setting we suggest a novel gradient estimate that combines two recent mechanism that are related to notion of…

Machine Learning · Computer Science 2025-03-06 Tehila Dahan , Kfir Y. Levy

Stochastic gradient descent (SGD) is one of the most popular algorithms in modern machine learning. The noise encountered in these applications is different from that in many theoretical analyses of stochastic gradient algorithms. In this…

Machine Learning · Statistics 2021-09-16 Stephan Wojtowytsch