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Stochastic gradient descent (SGD) optimization methods such as the plain vanilla SGD method and the popular Adam optimizer are nowadays the method of choice in the training of artificial neural networks (ANNs). Despite the remarkable…

Optimization and Control · Mathematics 2024-02-09 Arnulf Jentzen , Adrian Riekert

Many key problems in machine learning and data science are routinely modeled as optimization problems and solved via optimization algorithms. With the increase of the volume of data and the size and complexity of the statistical models used…

Optimization and Control · Mathematics 2020-08-28 Filip Hanzely

Despite substantial progress in the field of deep learning, overfitting persists as a critical challenge, and data augmentation has emerged as a particularly promising approach due to its capacity to enhance model generalization in various…

Computer Vision and Pattern Recognition · Computer Science 2023-08-16 Wen Liang , Youzhi Liang , Jianguo Jia

In the training of neural networks, adaptive moment estimation (Adam) typically converges fast but exhibits suboptimal generalization performance. A widely accepted explanation for its defect in generalization is that it often tends to…

Machine Learning · Computer Science 2026-03-10 Tao Shi , Liangming Chen , Long Jin , Mengchu Zhou

It is known that the standard stochastic gradient descent (SGD) optimization method, as well as accelerated and adaptive SGD optimization methods such as the Adam optimizer fail to converge if the learning rates do not converge to zero (as,…

Optimization and Control · Mathematics 2024-06-21 Steffen Dereich , 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

We propose a new variant of the Adam optimizer called MicroAdam that specifically minimizes memory overheads, while maintaining theoretical convergence guarantees. We achieve this by compressing the gradient information before it is fed…

Machine Learning · Computer Science 2024-11-06 Ionut-Vlad Modoranu , Mher Safaryan , Grigory Malinovsky , Eldar Kurtic , Thomas Robert , Peter Richtarik , Dan Alistarh

We introduce Gravity, another algorithm for gradient-based optimization. In this paper, we explain how our novel idea change parameters to reduce the deep learning model's loss. It has three intuitive hyper-parameters that the best values…

Machine Learning · Computer Science 2021-01-25 Dariush Bahrami , Sadegh Pouriyan Zadeh

Focusing on the practical configuration needs of optimization algorithms in deep learning, this article concentrates on five major algorithms: SGD, Mini-batch SGD, Momentum, Adam, and Lion. It systematically analyzes the core advantages,…

Machine Learning · Computer Science 2025-11-27 Deng Fucheng , Wang Wanjie , Gong Ao , Wang Xiaoqi , Wang Fan

Adaptive gradient-based optimization methods such as \textsc{Adagrad}, \textsc{Rmsprop}, and \textsc{Adam} are widely used in solving large-scale machine learning problems including deep learning. A number of schemes have been proposed in…

Machine Learning · Computer Science 2019-05-30 Parvin Nazari , Davoud Ataee Tarzanagh , George Michailidis

Sharpness aware minimization (SAM) optimizer has been extensively explored as it can generalize better for training deep neural networks via introducing extra perturbation steps to flatten the landscape of deep learning models. Integrating…

Machine Learning · Computer Science 2023-03-02 Hao Sun , Li Shen , Qihuang Zhong , Liang Ding , Shixiang Chen , Jingwei Sun , Jing Li , Guangzhong Sun , Dacheng Tao

We present a distributed generic algorithm called DAMS dedicated to adaptive optimization in distributed environments. Given a set of metaheuristic, the goal of DAMS is to coordinate their local execution on distributed nodes in order to…

Neural and Evolutionary Computing · Computer Science 2012-07-19 Bilel Derbel , Sébastien Verel

Sharpness-Aware Minimization (SAM) improves model generalization but doubles the computational cost of Stochastic Gradient Descent (SGD) by requiring twice the gradient calculations per optimization step. To mitigate this, we propose…

Computer Vision and Pattern Recognition · Computer Science 2025-10-07 Jiaxin Deng , Junbiao Pang

We consider practical data characteristics underlying federated learning, where unbalanced and non-i.i.d. data from clients have a block-cyclic structure: each cycle contains several blocks, and each client's training data follow…

Machine Learning · Computer Science 2020-02-19 Yucheng Ding , Chaoyue Niu , Yikai Yan , Zhenzhe Zheng , Fan Wu , Guihai Chen , Shaojie Tang , Rongfei Jia

Deep learning optimizers are optimization algorithms that enable deep neural networks to learn. The effectiveness of learning is highly dependent on the optimizer employed in the training process. Alongside the rapid advancement of deep…

Machine Learning · Computer Science 2025-09-24 Doğay Altınel

The memory challenges associated with training Large Language Models (LLMs) have become a critical concern, particularly when using the Adam optimizer. To address this issue, numerous memory-efficient techniques have been proposed, with…

Machine Learning · Computer Science 2025-02-12 Yiming Chen , Yuan Zhang , Yin Liu , Kun Yuan , Zaiwen Wen

Multidimensional scaling (MDS) is a popular dimensionality reduction techniques that has been widely used for network visualization and cooperative localization. However, the traditional stress minimization formulation of MDS necessitates…

Optimization and Control · Mathematics 2016-12-22 Ketan Rajawat , Sandeep Kumar

We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among…

Machine Learning · Computer Science 2015-10-27 Sixin Zhang , Anna Choromanska , Yann LeCun

Classical machine learning models such as deep neural networks are usually trained by using Stochastic Gradient Descent-based (SGD) algorithms. The classical SGD can be interpreted as a discretization of the stochastic gradient flow. In…

Optimization and Control · Mathematics 2023-10-03 Valentin Leplat , Daniil Merkulov , Aleksandr Katrutsa , Daniel Bershatsky , Olga Tsymboi , Ivan Oseledets

We present Amos, a stochastic gradient-based optimizer designed for training deep neural networks. It can be viewed as an Adam optimizer with theoretically supported, adaptive learning-rate decay and weight decay. A key insight behind Amos…

Machine Learning · Computer Science 2022-11-22 Ran Tian , Ankur P. Parikh