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Stochastic gradient descent (SGD) optimization methods are nowadays the method of choice for the training of deep neural networks (DNNs) in artificial intelligence systems. In practically relevant training problems, usually not the plain…

Optimization and Control · Mathematics 2024-08-01 Steffen Dereich , Arnulf Jentzen

Adaptive gradient-descent optimizers are the standard choice for training neural network models. Despite their faster convergence than gradient-descent and remarkable performance in practice, the adaptive optimizers are not as well…

Machine Learning · Computer Science 2024-07-18 Kushal Chakrabarti , Mayank Baranwal

When using large-batch training to speed up stochastic gradient descent, learning rates must adapt to new batch sizes in order to maximize speed-ups and preserve model quality. Re-tuning learning rates is resource intensive, while fixed…

Machine Learning · Computer Science 2020-07-13 Tyler B. Johnson , Pulkit Agrawal , Haijie Gu , Carlos Guestrin

Stochastic optimization plays a crucial role in the advancement of deep learning technologies. Over the decades, significant effort has been dedicated to improving the training efficiency and robustness of deep neural networks, via various…

Machine Learning · Computer Science 2024-08-21 Huixiu Jiang , Ling Yang , Yu Bao , Rutong Si , Sikun Yang

Although stochastic gradient descent (SGD) method and its variants (e.g., stochastic momentum methods, AdaGrad) are the choice of algorithms for solving non-convex problems (especially deep learning), there still remain big gaps between the…

Optimization and Control · Mathematics 2019-03-07 Zaiyi Chen , Zhuoning Yuan , Jinfeng Yi , Bowen Zhou , Enhong Chen , Tianbao Yang

Modern adaptive optimization methods, such as Adam and its variants, have emerged as the most widely used tools in deep learning over recent years. These algorithms offer automatic mechanisms for dynamically adjusting the update step based…

Machine Learning · Computer Science 2025-02-12 Son Nguyen , Bo Liu , Lizhang Chen , Qiang Liu

The success of deep learning can be attributed to various factors such as increase in computational power, large datasets, deep convolutional neural networks, optimizers etc. Particularly, the choice of optimizer affects the generalization,…

Machine Learning · Computer Science 2021-09-10 Anirudh Maiya , Inumella Sricharan , Anshuman Pandey , Srinivas K. S

Gradient descent (GD) based optimization methods are these days the standard tools to train deep neural networks in artificial intelligence systems. In optimization procedures in deep learning the employed optimizer is often not the…

Optimization and Control · Mathematics 2025-09-24 Steffen Dereich , Robin Graeber , Arnulf Jentzen , Adrian Riekert

Deep learning methods - consisting of a class of deep neural networks (DNNs) trained by a stochastic gradient descent (SGD) optimization method - are nowadays key tools to solve data driven supervised learning problems. Despite the great…

Machine Learning · Computer Science 2025-02-18 Thang Do , Sonja Hannibal , Arnulf Jentzen

Adaptive stochastic gradient methods such as AdaGrad have gained popularity in particular for training deep neural networks. The most commonly used and studied variant maintains a diagonal matrix approximation to second order information by…

Following the introduction of Adam, several novel adaptive optimizers for deep learning have been proposed. These optimizers typically excel in some tasks but may not outperform Adam uniformly across all tasks. In this work, we introduce…

Machine Learning · Computer Science 2024-06-18 Kaan Ozkara , Can Karakus , Parameswaran Raman , Mingyi Hong , Shoham Sabach , Branislav Kveton , Volkan Cevher

Neural network training is inherently sequential where the layers finish the forward propagation in succession, followed by the calculation and back-propagation of gradients (based on a loss function) starting from the last layer. The…

Machine Learning · Computer Science 2023-12-01 Vahid Janfaza , Shantanu Mandal , Farabi Mahmud , Abdullah Muzahid

Deep learning algorithms - typically consisting of a class of deep neural networks trained by a stochastic gradient descent (SGD) optimization method - are nowadays the key ingredients in many artificial intelligence (AI) systems and have…

Machine Learning · Computer Science 2024-07-12 Steffen Dereich , Robin Graeber , Arnulf Jentzen

In the paper, we propose a class of faster adaptive Gradient Descent Ascent (GDA) methods for solving the nonconvex-strongly-concave minimax problems by using the unified adaptive matrices, which include almost all existing coordinate-wise…

Optimization and Control · Mathematics 2023-02-22 Feihu Huang , Xidong Wu , Zhengmian Hu

This paper proposes an efficient optimizer called AdaPlus which integrates Nesterov momentum and precise stepsize adjustment on AdamW basis. AdaPlus combines the advantages of AdamW, Nadam, and AdaBelief and, in particular, does not…

Machine Learning · Computer Science 2023-12-27 Lei Guan

Despite the popularity of the Adam optimizer in practice, most theoretical analyses study Stochastic Gradient Descent (SGD) as a proxy for Adam, and little is known about how the solutions found by Adam differ. In this paper, we show that…

Machine Learning · Computer Science 2025-11-05 Xinghan Li , Haodong Wen , Kaifeng Lyu

Transformers are difficult to optimize with stochastic gradient descent (SGD) and largely rely on adaptive optimizers such as Adam. Despite their empirical success, the reasons behind Adam's superior performance over SGD remain poorly…

Machine Learning · Computer Science 2026-02-19 Akiyoshi Tomihari , Issei Sato

Adaptive gradient optimizers (AdaGrad), which dynamically adjust the learning rate based on iterative gradients, have emerged as powerful tools in deep learning. These adaptive methods have significantly succeeded in various deep learning…

Optimization and Control · Mathematics 2024-12-31 Ruinan Jin , Xiaoyu Wang , Baoxiang Wang

Adaptive optimizers, such as Adam, have achieved remarkable success in deep learning. A key component of these optimizers is the so-called preconditioning matrix, providing enhanced gradient information and regulating the step size of each…

Machine Learning · Computer Science 2024-12-10 Yun Yue , Zhiling Ye , Jiadi Jiang , Yongchao Liu , Ke Zhang

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…

Machine Learning · Computer Science 2020-06-12 Mahdi S. Hosseini , Konstantinos N. Plataniotis