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Stochastic gradient descent (SGD) is widely used in machine learning. Although being commonly viewed as a fast but not accurate version of gradient descent (GD), it always finds better solutions than GD for modern neural networks. In order…

Machine Learning · Computer Science 2018-08-17 Robert Kleinberg , Yuanzhi Li , Yang Yuan

The mini-batch stochastic gradient descent (SGD) algorithm is widely used in training machine learning models, in particular deep learning models. We study SGD dynamics under linear regression and two-layer linear networks, with an easy…

Optimization and Control · Mathematics 2020-04-29 Xin Qian , Diego Klabjan

The fluctuation effect of gradient expectation and variance caused by parameter update between consecutive iterations is neglected or confusing by current mainstream gradient optimization algorithms.Using this fluctuation effect, combined…

Machine Learning · Statistics 2022-02-23 Aixiang , Chen , Jinting Zhang , Zanbo Zhang , Zhihong Li

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

Selecting an effective step-size is a fundamental challenge in first-order optimization, especially for problems with non-Euclidean geometries. This paper presents a novel adaptive step-size strategy for optimization algorithms that rely on…

Optimization and Control · Mathematics 2025-10-14 Abbas Khademi , Antonio Silveti-Falls

This paper considers a general stochastic resource allocation problem that arises widely in wireless networks, cognitive radio, networks, smart-grid communications, and cross-layer design. The problem formulation involves expectations with…

Optimization and Control · Mathematics 2017-12-12 Amrit Singh Bedi , Ketan Rajawat

In this paper, we study the stochastic gradient descent (SGD) method for the nonconvex nonsmooth optimization, and propose an accelerated SGD method by combining the variance reduction technique with Nesterov's extrapolation technique.…

Optimization and Control · Mathematics 2019-02-18 Feihu Huang , Songcan Chen

Classical stochastic gradient methods are well suited for minimizing expected-value objective functions. However, they do not apply to the minimization of a nonlinear function involving expected values or a composition of two expected-value…

Machine Learning · Statistics 2014-11-17 Mengdi Wang , Ethan X. Fang , Han Liu

In this contribution, we present a full overview of the continuous stochastic gradient (CSG) method, including convergence results, step size rules and algorithmic insights. We consider optimization problems in which the objective function…

Optimization and Control · Mathematics 2023-03-23 Max Grieshammer , Lukas Pflug , Michael Stingl , Andrian Uihlein

Stochastic gradient methods enable learning probabilistic models from large amounts of data. While large step-sizes (learning rates) have shown to be best for least-squares (e.g., Gaussian noise) once combined with parameter averaging,…

Machine Learning · Statistics 2018-11-22 Dmitry Babichev , Francis Bach

Stochastic gradient descent (SGD) for strongly convex functions converges at the rate $\bO(1/k)$. However, achieving good results in practice requires tuning the parameters (for example the learning rate) of the algorithm. In this paper we…

Optimization and Control · Mathematics 2019-07-15 Adam M. Oberman , Mariana Prazeres

Many problems require to optimize empirical risk functions over large data sets. Gradient descent methods that calculate the full gradient in every descent step do not scale to such datasets. Various flavours of Stochastic Gradient Descent…

Machine Learning · Computer Science 2020-11-26 Francesco Cosentino , Harald Oberhauser , Alessandro Abate

Stochastic Gradient Descent (SGD) is among the simplest and most popular methods in optimization. The convergence rate for SGD has been extensively studied and tight analyses have been established for the running average scheme, but the…

Optimization and Control · Mathematics 2021-06-29 Daogao Liu , Zhou Lu

Recently, Loizou et al. (2021), proposed and analyzed stochastic gradient descent (SGD) with stochastic Polyak stepsize (SPS). The proposed SPS comes with strong convergence guarantees and competitive performance; however, it has two main…

Optimization and Control · Mathematics 2024-02-20 Antonio Orvieto , Simon Lacoste-Julien , Nicolas Loizou

Optimization algorithms are pivotal in advancing various scientific and industrial fields but often encounter obstacles such as trapping in local minima, saddle points, and plateaus (flat regions), which makes the convergence to reasonable…

Optimization and Control · Mathematics 2026-01-15 Amir M. Vahedi , Horea T. Ilies

We investigate the convergence rates and data sample sizes required for training a machine learning model using a stochastic gradient descent (SGD) algorithm, where data points are sampled based on either their loss value or uncertainty…

Machine Learning · Computer Science 2024-11-26 Daniel Haimovich , Dima Karamshuk , Fridolin Linder , Niek Tax , Milan Vojnovic

In this paper, we consider solving the distributed optimization problem over a multi-agent network under the communication restricted setting. We study a compressed decentralized stochastic gradient method, termed ``compressed exact…

Optimization and Control · Mathematics 2024-10-01 Kun Huang , Shi Pu

Stochastic Gradient Descent (SGD) has become popular for solving large scale supervised machine learning optimization problems such as SVM, due to their strong theoretical guarantees. While the closely related Dual Coordinate Ascent (DCA)…

Machine Learning · Statistics 2015-03-20 Shai Shalev-Shwartz , Tong Zhang

Stochastic Gradient Descent (SGD) is a known stochastic iterative method popular for large-scale convex optimization problems due to its simple implementation and scalability. Some objectives, such as those found in complex-valued neural…

Machine Learning · Computer Science 2026-05-26 Natanael Alpay , Emeric Battaglia

This paper considers a general data-fitting problem over a networked system, in which many computing nodes are connected by an undirected graph. This kind of problem can find many real-world applications and has been studied extensively in…

Machine Learning · Computer Science 2017-04-14 Ying Zhang