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Stochastic gradient descent (SGD) is commonly used for optimization in large-scale machine learning problems. Langford et al. (2009) introduce a sparse online learning method to induce sparsity via truncated gradient. With high-dimensional…

Machine Learning · Statistics 2017-05-10 Yuting Ma , Tian Zheng

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

Stochastic Gradient Langevin Dynamics (SGLD) is a popular variant of Stochastic Gradient Descent, where properly scaled isotropic Gaussian noise is added to an unbiased estimate of the gradient at each iteration. This modest change allows…

Machine Learning · Computer Science 2017-06-06 Maxim Raginsky , Alexander Rakhlin , Matus Telgarsky

Stochastic gradient descent (SGD) is a prevalent optimization technique for large-scale distributed machine learning. While SGD computation can be efficiently divided between multiple machines, communication typically becomes a bottleneck…

Machine Learning · Computer Science 2021-05-24 Dmitrii Avdiukhin , Grigory Yaroslavtsev

Following the same routine as [SSJ20], we continue to present the theoretical analysis for stochastic gradient descent with momentum (SGD with momentum) in this paper. Differently, for SGD with momentum, we demonstrate it is the two…

Machine Learning · Computer Science 2022-09-13 Bin Shi

The classical convergence analysis of SGD is carried out under the assumption that the norm of the stochastic gradient is uniformly bounded. While this might hold for some loss functions, it is violated for cases where the objective…

Optimization and Control · Mathematics 2019-11-12 Lam M. Nguyen , Phuong Ha Nguyen , Peter Richtárik , Katya Scheinberg , Martin Takáč , Marten van Dijk

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm…

Probability · Mathematics 2017-10-31 Justin Sirignano , Konstantinos Spiliopoulos

This paper analyzes the trajectories of stochastic gradient descent (SGD) to help understand the algorithm's convergence properties in non-convex problems. We first show that the sequence of iterates generated by SGD remains bounded and…

Optimization and Control · Mathematics 2020-06-22 Panayotis Mertikopoulos , Nadav Hallak , Ali Kavis , Volkan Cevher

Stochastic Gradient Descent (SGD) methods are prominent for training machine learning and deep learning models. The performance of these techniques depends on their hyperparameter tuning over time and varies for different models and…

Machine Learning · Statistics 2019-08-22 Tomer Lancewicki , Selcuk Kopru

Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…

Optimization and Control · Mathematics 2024-12-19 Andrey Sadchikov , Savelii Chezhegov , Aleksandr Beznosikov , Alexander Gasnikov

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

We study stochastic gradient descent (SGD) for composite optimization problems with $N$ sequential operators subject to perturbations in both the forward and backward passes. Unlike classical analyses that treat gradient noise as additive…

Optimization and Control · Mathematics 2026-02-25 Boao Kong , Hengrui Zhang , Kun Yuan

Stochastic gradient descent (SGD) is a simple and popular method to solve stochastic optimization problems which arise in machine learning. For strongly convex problems, its convergence rate was known to be O(\log(T)/T), by running SGD for…

Machine Learning · Computer Science 2015-03-19 Alexander Rakhlin , Ohad Shamir , Karthik Sridharan

Motivated by the problem of online canonical correlation analysis, we propose the \emph{Stochastic Scaled-Gradient Descent} (SSGD) algorithm for minimizing the expectation of a stochastic function over a generic Riemannian manifold. SSGD…

Machine Learning · Statistics 2022-01-25 Chris Junchi Li , Michael I. Jordan

We consider stochastic gradient descent (SGD) for least-squares regression with potentially several passes over the data. While several passes have been widely reported to perform practically better in terms of predictive performance on…

Machine Learning · Computer Science 2018-11-26 Loucas Pillaud-Vivien , Alessandro Rudi , Francis Bach

Accelerated stochastic gradient descent (ASGD) is a workhorse in deep learning and often achieves better generalization performance than SGD. However, existing optimization theory can only explain the faster convergence of ASGD, but cannot…

Machine Learning · Computer Science 2023-11-27 Xuheng Li , Yihe Deng , Jingfeng Wu , Dongruo Zhou , Quanquan Gu

Stochastic Gradient Descent (SGD) is one of the many iterative optimization methods that are widely used in solving machine learning problems. These methods display valuable properties and attract researchers and industrial machine learning…

Machine Learning · Computer Science 2023-10-04 Farshed Abdukhakimov , Chulu Xiang , Dmitry Kamzolov , Martin Takáč

While momentum-based accelerated variants of stochastic gradient descent (SGD) are widely used when training machine learning models, there is little theoretical understanding on the generalization error of such methods. In this work, we…

Machine Learning · Computer Science 2024-01-17 Ali Ramezani-Kebrya , Kimon Antonakopoulos , Volkan Cevher , Ashish Khisti , Ben Liang

Stochastic gradient descent (SGD) with mini-batching is a standard tool in large-scale optimization, yet its theoretical properties under heavy-tailed gradient noise remain largely unexplored. In this paper we study SGD with increasing…

Probability · Mathematics 2026-05-11 Bartosz Glowacki , Rafal Kulik , Philippe Soulier

Iterative procedures for parameter estimation based on stochastic gradient descent allow the estimation to scale to massive data sets. However, in both theory and practice, they suffer from numerical instability. Moreover, they are…

Methodology · Statistics 2016-06-08 Panos Toulis , Dustin Tran , Edoardo M. Airoldi