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First-order methods such as stochastic gradient descent (SGD) are currently the standard algorithm for training deep neural networks. Second-order methods, despite their better convergence rate, are rarely used in practice due to the…

Machine Learning · Computer Science 2019-09-26 Tianle Cai , Ruiqi Gao , Jikai Hou , Siyu Chen , Dong Wang , Di He , Zhihua Zhang , Liwei Wang

Stochastic Gradient Descent (SGD) is the central workhorse for training modern CNNs. Although giving impressive empirical performance it can be slow to converge. In this paper we explore a novel strategy for training a CNN using an…

Machine Learning · Computer Science 2017-12-15 Chen Huang , Chen Kong , Simon Lucey

We propose a distributed approach to train deep neural networks (DNNs), which has guaranteed convergence theoretically and great scalability empirically: close to 6 times faster on instance of ImageNet data set when run with 6 machines. The…

Machine Learning · Statistics 2016-10-04 Abhimanu Kumar , Pengtao Xie , Junming Yin , Eric P. Xing

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

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

Stochastic Gradient Descent (SGD) is arguably the most important single algorithm in modern machine learning. Although SGD with unbiased gradient estimators has been studied extensively over at least half a century, SGD variants relying on…

Machine Learning · Computer Science 2023-05-26 Yury Demidovich , Grigory Malinovsky , Igor Sokolov , Peter Richtárik

Deep learning networks are typically trained by Stochastic Gradient Descent (SGD) methods that iteratively improve the model parameters by estimating a gradient on a very small fraction of the training data. A major roadblock faced when…

Machine Learning · Computer Science 2020-06-11 Tao Lin , Lingjing Kong , Sebastian U. Stich , Martin Jaggi

We describe a computationally efficient, stochastic graph-regularization technique that can be utilized for the semi-supervised training of deep neural networks in a parallel or distributed setting. We utilize a technique, first described…

Machine Learning · Statistics 2018-05-31 Sunil Thulasidasan , Jeffrey Bilmes , Garrett Kenyon

With an increasing demand for training powers for deep learning algorithms and the rapid growth of computation resources in data centers, it is desirable to dynamically schedule different distributed deep learning tasks to maximize resource…

Machine Learning · Computer Science 2019-05-03 Haibin Lin , Hang Zhang , Yifei Ma , Tong He , Zhi Zhang , Sheng Zha , Mu Li

In this work, we reveal a strong implicit bias of stochastic gradient descent (SGD) that drives overly expressive networks to much simpler subnetworks, thereby dramatically reducing the number of independent parameters, and improving…

Machine Learning · Computer Science 2024-05-30 Feng Chen , Daniel Kunin , Atsushi Yamamura , Surya Ganguli

We consider the setting where a master wants to run a distributed stochastic gradient descent (SGD) algorithm on $n$ workers, each having a subset of the data. Distributed SGD may suffer from the effect of stragglers, i.e., slow or…

Machine Learning · Computer Science 2022-08-08 Serge Kas Hanna , Rawad Bitar , Parimal Parag , Venkat Dasari , Salim El Rouayheb

Stochastic gradient descent (SGD) and its many variants are the widespread optimization algorithms for training deep neural networks. However, SGD suffers from inevitable drawbacks, including vanishing gradients, lack of theoretical…

Machine Learning · Computer Science 2024-01-09 Zeinab Ebrahimi , Gustavo Batista , Mohammad Deghat

Convergence detection of iterative stochastic optimization methods is of great practical interest. This paper considers stochastic gradient descent (SGD) with a constant learning rate and momentum. We show that there exists a transient…

Machine Learning · Computer Science 2020-08-28 Jerry Chee , Ping Li

Stochastic gradient descent (SGD) method is popular for solving non-convex optimization problems in machine learning. This work investigates SGD from a viewpoint of graduated optimization, which is a widely applied approach for non-convex…

Optimization and Control · Mathematics 2023-08-15 Da Li , Jingjing Wu , Qingrun Zhang

Stochastic gradient descent (SGD) is widely used in deep learning due to its computational efficiency, but a complete understanding of why SGD performs so well remains a major challenge. It has been observed empirically that most…

Machine Learning · Statistics 2022-06-20 Carmina Fjellström , Kaj Nyström

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…

Machine Learning · Statistics 2023-06-23 Gerard Ben Arous , Reza Gheissari , Aukosh Jagannath

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

With the fast development of deep learning, it has become common to learn big neural networks using massive training data. Asynchronous Stochastic Gradient Descent (ASGD) is widely adopted to fulfill this task for its efficiency, which is,…

Machine Learning · Computer Science 2020-02-19 Shuxin Zheng , Qi Meng , Taifeng Wang , Wei Chen , Nenghai Yu , Zhi-Ming Ma , Tie-Yan Liu

The performance of mini-batch stochastic gradient descent (SGD) strongly depends on setting the batch size and learning rate to minimize the empirical loss in training the deep neural network. In this paper, we present theoretical analyses…

Machine Learning · Computer Science 2025-02-17 Hikaru Umeda , Hideaki Iiduka

Over the last four decades, the amazing success of deep learning has been driven by the use of Stochastic Gradient Descent (SGD) as the main optimization technique. The default implementation for the computation of the gradient for SGD is…

Neural and Evolutionary Computing · Computer Science 2024-12-31 Qianli Liao , Liu Ziyin , Yulu Gan , Brian Cheung , Mark Harnett , Tomaso Poggio