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The training of modern deep learning neural network calls for large amounts of computation, which is often provided by GPUs or other specific accelerators. To scale out to achieve faster training speed, two update algorithms are mainly…

Machine Learning · Computer Science 2020-05-15 Yemao Xu , Dezun Dong , Weixia Xu , Xiangke Liao

In this paper, we revisit stochastic gradient descent (SGD) with AdaGrad-type preconditioning. Our contributions are twofold. First, we develop a unified convergence analysis of SGD with adaptive preconditioning under anisotropic or matrix…

Machine Learning · Computer Science 2025-07-01 Dmitry Kovalev

Stochastic gradient descent (SGD) is one of the most widely used algorithms for large scale optimization problems. While classical theoretical analysis of SGD for convex problems studies (suffix) \emph{averages} of iterates and obtains…

Optimization and Control · Mathematics 2019-05-30 Prateek Jain , Dheeraj Nagaraj , Praneeth Netrapalli

Modern machine learning focuses on highly expressive models that are able to fit or interpolate the data completely, resulting in zero training loss. For such models, we show that the stochastic gradients of common loss functions satisfy a…

Machine Learning · Computer Science 2019-04-09 Sharan Vaswani , Francis Bach , Mark Schmidt

A common pursuit in modern statistical learning is to attain satisfactory generalization out of the source data distribution (OOD). In theory, the challenge remains unsolved even under the canonical setting of covariate shift for the linear…

Machine Learning · Statistics 2025-02-14 Yuanshi Liu , Haihan Zhang , Qian Chen , Cong Fang

Stochastic gradient descent (SGD) optimization algorithms are key ingredients in a series of machine learning applications. In this article we perform a rigorous strong error analysis for SGD optimization algorithms. In particular, we prove…

Numerical Analysis · Mathematics 2020-10-05 Arnulf Jentzen , Benno Kuckuck , Ariel Neufeld , Philippe von Wurstemberger

Asynchronous stochastic gradient descent (SGD) enables scalable distributed training but suffers from gradient staleness. Existing mitigation strategies, such as delay-adaptive learning rates and staleness-aware filtering, typically…

Machine Learning · Computer Science 2026-05-15 Tehila Dahan , Roie Reshef , Sharon Goldstein , Kfir Y. Levy

We consider the noisy matrix sensing problem in the over-parameterization setting, where the estimated rank $r$ is larger than the true rank $r_\star$ of the target matrix $X_\star$. Specifically, our main objective is to recover a matrix $…

Machine Learning · Computer Science 2025-06-03 Zhiyu Liu , Zhi Han , Yandong Tang , Shaojie Tang , Yao Wang

This paper studies the problem of recovering a low-rank matrix from several noisy random linear measurements. We consider the setting where the rank of the ground-truth matrix is unknown a priori and use an objective function built from a…

Optimization and Control · Mathematics 2025-07-29 Lijun Ding , Zhen Qin , Liwei Jiang , Jinxin Zhou , Zhihui Zhu

Neural network optimization remains one of the most consequential yet poorly understood challenges in modern AI research, where improvements in training algorithms can lead to enhanced feature learning in foundation models,…

Machine Learning · Computer Science 2025-12-23 Ansh Nagwekar

We study the space complexity of solving the bias-regularized SVM problem in the streaming model. This is a classic supervised learning problem that has drawn lots of attention, including for developing fast algorithms for solving the…

Data Structures and Algorithms · Computer Science 2020-07-08 Alexandr Andoni , Collin Burns , Yi Li , Sepideh Mahabadi , David P. Woodruff

Mini-batch stochastic gradient descent (SGD) and variants thereof approximate the objective function's gradient with a small number of training examples, aka the batch size. Small batch sizes require little computation for each model update…

Machine Learning · Computer Science 2023-09-28 Scott Sievert , Shrey Shah

The implementation of a vast majority of machine learning (ML) algorithms boils down to solving a numerical optimization problem. In this context, Stochastic Gradient Descent (SGD) methods have long proven to provide good results, both in…

Distributed, Parallel, and Cluster Computing · Computer Science 2015-10-06 Janis Keuper , Franz-Josef Pfreundt

Stochastic gradient descent (SGD) performed in an asynchronous manner plays a crucial role in training large-scale machine learning models. However, the generalization performance of asynchronous delayed SGD, which is an essential metric…

Machine Learning · Computer Science 2025-05-27 Xiaoge Deng , Li Shen , Shengwei Li , Tao Sun , Dongsheng Li , Dacheng Tao

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

The paper looks at a scaled variant of the stochastic gradient descent algorithm for the matrix completion problem. Specifically, we propose a novel matrix-scaling of the partial derivatives that acts as an efficient preconditioning for the…

Machine Learning · Computer Science 2016-10-06 Bamdev Mishra , Rodolphe Sepulchre

Stochastic gradient descent (SGD) is a promising method for solving large-scale inverse problems, due to its excellent scalability with respect to data size. The current mathematical theory in the lens of regularization theory predicts that…

Optimization and Control · Mathematics 2021-08-10 Bangti Jin , Zehui Zhou , Jun Zou

We study gradient descent (GD) with a constant stepsize for $\ell_2$-regularized logistic regression with linearly separable data. Classical theory suggests small stepsizes to ensure monotonic reduction of the optimization objective,…

Machine Learning · Statistics 2025-11-04 Jingfeng Wu , Pierre Marion , Peter Bartlett

We analyze (stochastic) gradient descent (SGD) with delayed updates on smooth quasi-convex and non-convex functions and derive concise, non-asymptotic, convergence rates. We show that the rate of convergence in all cases consists of two…

Machine Learning · Computer Science 2021-06-17 Sebastian U. Stich , Sai Praneeth Karimireddy