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Related papers: SGD: General Analysis and Improved Rates

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Theoretically understanding stochastic gradient descent (SGD) in overparameterized models has led to the development of several optimization algorithms that are widely used in practice today. Recent work by~\citet{zou2021benign} provides…

Machine Learning · Computer Science 2025-06-19 Alexandru Meterez , Depen Morwani , Costin-Andrei Oncescu , Jingfeng Wu , Cengiz Pehlevan , Sham Kakade

Machine learning models trained with \emph{stochastic} gradient descent (SGD) can generalize better than those trained with deterministic gradient descent (GD). In this work, we study SGD's impact on generalization through the lens of the…

Machine Learning · Computer Science 2025-12-09 Hongjian Lan , Yucong Liu , Florian Schäfer

The non-asymptotic analysis of Stochastic Gradient Descent (SGD) typically yields bounds that decompose into a bias term and a variance term. In this work, we focus on the bias component and study the extent to which SGD can match the…

Optimization and Control · Mathematics 2026-02-02 Daniel Cortild , Lucas Ketels , Juan Peypouquet , Guillaume Garrigos

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 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

Structured non-convex learning problems, for which critical points have favorable statistical properties, arise frequently in statistical machine learning. Algorithmic convergence and statistical estimation rates are well-understood for…

Machine Learning · Statistics 2020-07-31 Lu Yu , Krishnakumar Balasubramanian , Stanislav Volgushev , Murat A. Erdogdu

We propose a mini-batching scheme for improving the theoretical complexity and practical performance of semi-stochastic gradient descent applied to the problem of minimizing a strongly convex composite function represented as the sum of an…

Machine Learning · Computer Science 2014-10-20 Jakub Konečný , Jie Liu , Peter Richtárik , Martin Takáč

We develop and analyze a new algorithm for empirical risk minimization, which is the key paradigm for training supervised machine learning models. Our method---SAGD---is based on a probabilistic interpolation of SAGA and gradient descent…

Optimization and Control · Mathematics 2020-04-03 Adel Bibi , Alibek Sailanbayev , Bernard Ghanem , Robert Mansel Gower , Peter Richtárik

The stochastic gradient descent (SGD) method and its variants are algorithms of choice for many Deep Learning tasks. These methods operate in a small-batch regime wherein a fraction of the training data, say $32$-$512$ data points, is…

Machine Learning · Computer Science 2017-02-13 Nitish Shirish Keskar , Dheevatsa Mudigere , Jorge Nocedal , Mikhail Smelyanskiy , Ping Tak Peter Tang

For infinitesimal learning rates, stochastic gradient descent (SGD) follows the path of gradient flow on the full batch loss function. However moderately large learning rates can achieve higher test accuracies, and this generalization…

Machine Learning · Computer Science 2021-01-29 Samuel L. Smith , Benoit Dherin , David G. T. Barrett , Soham De

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 descent (SGD) and its variants are the main workhorses for solving large-scale optimization problems with nonconvex objective functions. Although the convergence of SGDs in the (strongly) convex case is well-understood,…

Machine Learning · Computer Science 2023-10-20 Aritra Dutta , El Houcine Bergou , Soumia Boucherouite , Nicklas Werge , Melih Kandemir , Xin Li

This paper presents a novel adaptation of the Stochastic Gradient Descent (SGD), termed AdaBatchGrad. This modification seamlessly integrates an adaptive step size with an adjustable batch size. An increase in batch size and a decrease in…

Machine Learning · Computer Science 2024-02-09 Petr Ostroukhov , Aigerim Zhumabayeva , Chulu Xiang , Alexander Gasnikov , Martin Takáč , Dmitry Kamzolov

Stochastic gradient descent (SGD) is the optimization algorithm of choice in many machine learning applications such as regularized empirical risk minimization and training deep neural networks. The classical convergence analysis of SGD is…

Optimization and Control · Mathematics 2018-07-10 Lam M. Nguyen , Phuong Ha Nguyen , Marten van Dijk , Peter Richtárik , Katya Scheinberg , Martin Takáč

In distributed learning, local SGD (also known as federated averaging) and its simple baseline minibatch SGD are widely studied optimization methods. Most existing analyses of these methods assume independent and unbiased gradient estimates…

Machine Learning · Computer Science 2022-03-24 Chulhee Yun , Shashank Rajput , Suvrit Sra

Stochastic gradient descent (SGD) is the workhorse of modern machine learning. Sometimes, there are many different potential gradient estimators that can be used. When so, choosing the one with the best tradeoff between cost and variance is…

Machine Learning · Computer Science 2020-10-23 Tomas Geffner , Justin Domke

Stochastic gradient descent (SGD) is a foundational algorithm for large-scale statistical learning and stochastic optimization. However, statistical inference based on SGD iterates remains challenging when stochastic gradients have infinite…

Machine Learning · Statistics 2026-05-26 Jose Blanchet , Peter Glynn , Wenhao Yang

It is often observed that stochastic gradient descent (SGD) and its variants implicitly select a solution with good generalization performance; such implicit bias is often characterized in terms of the sharpness of the minima. Kleinberg et…

Machine Learning · Statistics 2024-05-28 Atsushi Nitanda , Ryuhei Kikuchi , Shugo Maeda , Denny Wu

We analyze asynchronous-type algorithms for distributed SGD in the heterogeneous setting, where each worker has its own computation and communication speeds, as well as data distribution. In these algorithms, workers compute possibly stale…

Machine Learning · Computer Science 2023-11-01 Rustem Islamov , Mher Safaryan , Dan Alistarh

We consider the minimization of an objective function given access to unbiased estimates of its gradient through stochastic gradient descent (SGD) with constant step-size. While the detailed analysis was only performed for quadratic…

Machine Learning · Statistics 2018-04-12 Aymeric Dieuleveut , Alain Durmus , Francis Bach