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Stochastic Gradient Descent (SGD) is a popular tool in training large-scale machine learning models. Its performance, however, is highly variable, depending crucially on the choice of the step sizes. Accordingly, a variety of strategies for…

Machine Learning · Statistics 2021-06-11 Xiaoyu Li , Zhenxun Zhuang , Francesco Orabona

This paper presents a methodology for selecting the mini-batch size that minimizes Stochastic Gradient Descent (SGD) learning time for single and multiple learner problems. By decoupling algorithmic analysis issues from hardware and…

Machine Learning · Computer Science 2019-11-18 Michael P. Perrone , Haidar Khan , Changhoan Kim , Anastasios Kyrillidis , Jerry Quinn , Valentina Salapura

It has been experimentally observed that the efficiency of distributed training with stochastic gradient (SGD) depends decisively on the batch size and -- in asynchronous implementations -- on the gradient staleness. Especially, it has been…

Machine Learning · Computer Science 2021-03-04 Sebastian U. Stich , Amirkeivan Mohtashami , Martin Jaggi

We give a new separation result between the generalization performance of stochastic gradient descent (SGD) and of full-batch gradient descent (GD) in the fundamental stochastic convex optimization model. While for SGD it is well-known that…

Machine Learning · Computer Science 2021-07-01 Idan Amir , Tomer Koren , Roi Livni

We analyze in a closed form the learning dynamics of stochastic gradient descent (SGD) for a single-layer neural network classifying a high-dimensional Gaussian mixture where each cluster is assigned one of two labels. This problem provides…

Machine Learning · Computer Science 2022-03-28 Francesca Mignacco , Florent Krzakala , Pierfrancesco Urbani , Lenka Zdeborová

Geometric median (\textsc{Gm}) is a classical method in statistics for achieving a robust estimation of the uncorrupted data; under gross corruption, it achieves the optimal breakdown point of 0.5. However, its computational complexity…

Machine Learning · Computer Science 2021-06-17 Anish Acharya , Abolfazl Hashemi , Prateek Jain , Sujay Sanghavi , Inderjit S. Dhillon , Ufuk Topcu

Stochastic Gradient Descent (SGD) is an out-of-equilibrium algorithm used extensively to train artificial neural networks. However very little is known on to what extent SGD is crucial for to the success of this technology and, in…

Machine Learning · Computer Science 2023-12-19 Persia Jana Kamali , Pierfrancesco Urbani

We introduce a general framework for nonlinear stochastic gradient descent (SGD) for the scenarios when gradient noise exhibits heavy tails. The proposed framework subsumes several popular nonlinearity choices, like clipped, normalized,…

Optimization and Control · Mathematics 2022-04-07 Dusan Jakovetic , Dragana Bajovic , Anit Kumar Sahu , Soummya Kar , Nemanja Milosevic , Dusan Stamenkovic

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 a widely deployed optimization procedure throughout data-driven and simulation-driven disciplines, which has drawn a substantial interest in understanding its global behavior across a broad class of…

Optimization and Control · Mathematics 2021-04-02 Vivak Patel , Shushu Zhang

Previous works on stochastic gradient descent (SGD) often focus on its success. In this work, we construct worst-case optimization problems illustrating that, when not in the regimes that the previous works often assume, SGD can exhibit…

Machine Learning · Computer Science 2023-05-30 Liu Ziyin , Botao Li , James B. Simon , Masahito Ueda

We begin by briefly surveying some results on the convergence of the Stochastic Gradient Descent (SGD) Method, proved in a companion paper by the present authors. These results are based on viewing SGD as a version of Stochastic…

Machine Learning · Statistics 2025-09-10 Rajeeva L. Karandikar , M. Vidyasagar

We present a convergence rate analysis for biased stochastic gradient descent (SGD), where individual gradient updates are corrupted by computation errors. We develop stochastic quadratic constraints to formulate a small linear matrix…

Optimization and Control · Mathematics 2020-03-31 Bin Hu , Peter Seiler , Laurent Lessard

Most results on Stochastic Gradient Descent (SGD) in the convex and smooth setting are presented under the form of bounds on the ergodic function value gap. It is an open question whether bounds can be derived directly on the last iterate…

Optimization and Control · Mathematics 2025-07-21 Guillaume Garrigos , Daniel Cortild , Lucas Ketels , Juan Peypouquet

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…

Machine Learning · Computer Science 2020-03-04 Achraf Bahamou , Donald Goldfarb

The stability and generalization of stochastic gradient-based methods provide valuable insights into understanding the algorithmic performance of machine learning models. As the main workhorse for deep learning, stochastic gradient descent…

Machine Learning · Statistics 2021-02-24 Tao Sun , Dongsheng Li , Bao Wang

The stochastic gradient descent (SGD) algorithm has been widely used to optimize deep Cox neural network (Cox-NN) by updating model parameters using mini-batches of data. We show that SGD aims to optimize the average of mini-batch…

Machine Learning · Statistics 2026-04-16 Lang Zeng , Weijing Tang , Zhao Ren , Ying Ding

In this work we establish the first linear convergence result for the stochastic heavy ball method. The method performs SGD steps with a fixed stepsize, amended by a heavy ball momentum term. In the analysis, we focus on minimizing the…

Optimization and Control · Mathematics 2017-12-27 Nicolas Loizou , Peter Richtárik

Stochastic gradient descent (SGD) is the main algorithm behind a large body of work in machine learning. In many cases, constraints are enforced via projections, leading to projected stochastic gradient algorithms. In recent years, a large…

Optimization and Control · Mathematics 2025-10-06 Yuping Zheng , Andrew Lamperski

Stochastic gradient descent (SGD) is a pillar of modern machine learning, serving as the go-to optimization algorithm for a diverse array of problems. While the empirical success of SGD is often attributed to its computational efficiency…

Machine Learning · Statistics 2022-06-16 Courtney Paquette , Elliot Paquette , Ben Adlam , Jeffrey Pennington