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Multi-epoch, small-batch, Stochastic Gradient Descent (SGD) has been the method of choice for learning with large over-parameterized models. A popular theory for explaining why SGD works well in practice is that the algorithm has an…

机器学习 · 计算机科学 2021-07-13 Satyen Kale , Ayush Sekhari , Karthik Sridharan

Novel convergence analyses are presented of Riemannian stochastic gradient descent (RSGD) on a Hadamard manifold. RSGD is the most basic Riemannian stochastic optimization algorithm and is used in many applications in the field of machine…

最优化与控制 · 数学 2023-12-14 Hiroyuki Sakai , Hideaki Iiduka

The dynamical stability of optimization methods at the vicinity of minima of the loss has recently attracted significant attention. For gradient descent (GD), stable convergence is possible only to minima that are sufficiently flat w.r.t.…

机器学习 · 计算机科学 2024-06-18 Rotem Mulayoff , Tomer Michaeli

Local SGD is a popular optimization method in distributed learning, often outperforming other algorithms in practice, including mini-batch SGD. Despite this success, theoretically proving the dominance of local SGD in settings with…

Distributed stochastic gradient descent (SGD) approach has been widely used in large-scale deep learning, and the gradient collective method is vital to ensure the training scalability of the distributed deep learning system. Collective…

分布式、并行与集群计算 · 计算机科学 2021-11-29 Keshi Ge , Yongquan Fu , Zhiquan Lai , Xiaoge Deng , Dongsheng Li

Distributed stochastic gradient descent (SGD) is essential for scaling the machine learning algorithms to a large number of computing nodes. However, the infrastructures variability such as high communication delay or random node slowdown…

机器学习 · 计算机科学 2020-02-25 Jianyu Wang , Hao Liang , Gauri Joshi

In this work we apply model averaging to parallel training of deep neural network (DNN). Parallelization is done in a model averaging manner. Data is partitioned and distributed to different nodes for local model updates, and model…

机器学习 · 计算机科学 2018-07-03 Hang Su , Haoyu Chen

The convergence speed of stochastic gradient descent (SGD) can be improved by actively selecting mini-batches. We explore sampling schemes where similar data points are less likely to be selected in the same mini-batch. In particular, we…

机器学习 · 统计学 2018-06-21 Cheng Zhang , Cengiz Öztireli , Stephan Mandt , Giampiero Salvi

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…

机器学习 · 计算机科学 2023-05-30 Liu Ziyin , Botao Li , James B. Simon , Masahito Ueda

We study optimization algorithms based on variance reduction for stochastic gradient descent (SGD). Remarkable recent progress has been made in this direction through development of algorithms like SAG, SVRG, SAGA. These algorithms have…

机器学习 · 计算机科学 2016-01-26 Sashank J. Reddi , Ahmed Hefny , Suvrit Sra , Barnabás Póczos , Alex Smola

Stochastic gradient descent (SGD) and its variants are widely used and highly effective optimization methods in machine learning, especially for neural network training. By using a single datum or a small subset of the data, selected…

数值分析 · 数学 2026-01-21 Bangti Jin , Zeljko Kereta , Yuxin Xia

Stochastic gradient descent (SGD) is a popular and efficient method with wide applications in training deep neural nets and other nonconvex models. While the behavior of SGD is well understood in the convex learning setting, the existing…

机器学习 · 计算机科学 2019-12-16 Yunwen Lei , Ting Hu , Guiying Li , Ke Tang

Neural network has attracted great attention for a long time and many researchers are devoted to improve the effectiveness of neural network training algorithms. Though stochastic gradient descent (SGD) and other explicit gradient-based…

最优化与控制 · 数学 2020-02-11 Ren Liu , Xiaoqun Zhang

In this work we consider stochastic gradient descent (SGD) for solving linear inverse problems in Banach spaces. SGD and its variants have been established as one of the most successful optimisation methods in machine learning, imaging and…

机器学习 · 计算机科学 2023-02-13 Z. Kereta , B. Jin

We introduce Gradient Agreement Filtering (GAF) to improve on gradient averaging in distributed deep learning optimization. Traditional distributed data-parallel stochastic gradient descent involves averaging gradients of microbatches to…

机器学习 · 计算机科学 2024-12-31 Francois Chaubard , Duncan Eddy , Mykel J. Kochenderfer

In deep learning, mini-batch training is commonly used to optimize network parameters. However, the traditional mini-batch method may not learn the under-represented samples and complex patterns in the data, leading to a longer time for…

计算机视觉与模式识别 · 计算机科学 2023-04-10 Subin Sahayam , John Zakkam , Umarani Jayaraman

The choice of step-size used in Stochastic Gradient Descent (SGD) optimization is empirically selected in most training procedures. Moreover, the use of scheduled learning techniques such as Step-Decaying, Cyclical-Learning, and Warmup to…

机器学习 · 计算机科学 2020-06-12 Mahdi S. Hosseini , Konstantinos N. Plataniotis

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…

机器学习 · 计算机科学 2022-03-23 Amirkeivan Mohtashami , Martin Jaggi , Sebastian U. Stich

Hogwild! implements asynchronous Stochastic Gradient Descent (SGD) where multiple threads in parallel access a common repository containing training data, perform SGD iterations and update shared state that represents a jointly learned…

机器学习 · 计算机科学 2021-03-02 Marten van Dijk , Nhuong V. Nguyen , Toan N. Nguyen , Lam M. Nguyen , Quoc Tran-Dinh , Phuong Ha Nguyen

Stochastic gradient descent (SGD) is widely believed to perform implicit regularization when used to train deep neural networks, but the precise manner in which this occurs has thus far been elusive. We prove that SGD minimizes an average…

机器学习 · 计算机科学 2018-01-17 Pratik Chaudhari , Stefano Soatto