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We introduce Adam, an algorithm for first-order gradient-based optimization of stochastic objective functions, based on adaptive estimates of lower-order moments. The method is straightforward to implement, is computationally efficient, has…

Machine Learning · Computer Science 2017-01-31 Diederik P. Kingma , Jimmy Ba

In this paper, we introduce StochGradAdam, a novel optimizer designed as an extension of the Adam algorithm, incorporating stochastic gradient sampling techniques to improve computational efficiency while maintaining robust performance.…

Machine Learning · Computer Science 2025-03-19 Juyoung Yun

Adaptive gradient optimization methods, such as Adam, are prevalent in training deep neural networks across diverse machine learning tasks due to their ability to achieve faster convergence. However, these methods often suffer from…

Machine Learning · Computer Science 2025-02-12 Abulikemu Abuduweili , Changliu Liu

Machine learning algorithms aim to find patterns from observations, which may include some noise, especially in robotics domain. To perform well even with such noise, we expect them to be able to detect outliers and discard them when…

Machine Learning · Computer Science 2020-03-04 Wendyam Eric Lionel Ilboudo , Taisuke Kobayashi , Kenji Sugimoto

In this paper, we investigate the popular deep learning optimization routine, Adam, from the perspective of statistical moments. While Adam is an adaptive lower-order moment based (of the stochastic gradient) method, we propose an extension…

Machine Learning · Computer Science 2019-10-16 Zhanhong Jiang , Aditya Balu , Sin Yong Tan , Young M Lee , Chinmay Hegde , Soumik Sarkar

Averaging techniques such as Ruppert--Polyak averaging and exponential movering averaging (EMA) are powerful approaches to accelerate optimization procedures of stochastic gradient descent (SGD) optimization methods such as the popular ADAM…

Optimization and Control · Mathematics 2025-05-29 Arnulf Jentzen , Julian Kranz , Adrian Riekert

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

Machine Learning · Computer Science 2017-11-23 Haiping Huang , Taro Toyoizumi

Adam-type algorithms have become a preferred choice for optimisation in the deep learning setting, however, despite success, their convergence is still not well understood. To this end, we introduce a unified framework for Adam-type…

Machine Learning · Computer Science 2024-09-24 Yiming Jiang , Jinlan Liu , Dongpo Xu , Danilo P. Mandic

Adam is a popular variant of stochastic gradient descent for finding a local minimizer of a function. In the constant stepsize regime, assuming that the objective function is differentiable and non-convex, we establish the convergence in…

Machine Learning · Statistics 2020-05-15 Anas Barakat , Pascal Bianchi

In this paper, we propose a new first-order gradient-based algorithm to train deep neural networks. We first introduce the sign operation of stochastic gradients (as in sign-based methods, e.g., SIGN-SGD) into ADAM, which is called as…

Computer Vision and Pattern Recognition · Computer Science 2019-07-23 Dong Wang , Yicheng Liu , Wenwo Tang , Fanhua Shang , Hongying Liu , Qigong Sun , Licheng Jiao

This paper establishes a mathematical foundation for the Adam optimizer, elucidating its connection to natural gradient descent through Riemannian and information geometry. We provide an accessible and detailed analysis of the diagonal…

Machine Learning · Computer Science 2024-09-05 Dongseong Hwang

The adaptive moment estimation (Adam) optimizer proposed by Kingma & Ba (2014) is presumably the most popular stochastic gradient descent (SGD) optimization method for the training of deep neural networks (DNNs) in artificial intelligence…

Machine Learning · Computer Science 2026-03-20 Steffen Dereich , Thang Do , Arnulf Jentzen

Gradient-based first-order adaptive optimization methods such as the Adam optimizer are prevalent in training artificial networks, achieving the state-of-the-art results. This work attempts to answer the question whether it is viable for…

Neural and Evolutionary Computing · Computer Science 2022-12-20 Yukun Yang , Peng Li

We present an optimizer which uses Bayesian optimization to tune the system parameters of distributed stochastic gradient descent (SGD). Given a specific context, our goal is to quickly find efficient configurations which appropriately…

Machine Learning · Statistics 2016-12-04 Valentin Dalibard , Michael Schaarschmidt , Eiko Yoneki

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

Adam is a widely used stochastic optimization method for deep learning applications. While practitioners prefer Adam because it requires less parameter tuning, its use is problematic from a theoretical point of view since it may not…

Machine Learning · Computer Science 2020-11-25 Mingrui Liu , Wei Zhang , Francesco Orabona , Tianbao Yang

Decentralized optimization to minimize a finite sum of functions over a network of nodes has been a significant focus within control and signal processing research due to its natural relevance to optimal control and signal estimation…

Machine Learning · Computer Science 2020-09-15 Ran Xin , Shi Pu , Angelia Nedić , Usman A. Khan

The vast majority of successful deep neural networks are trained using variants of stochastic gradient descent (SGD) algorithms. Recent attempts to improve SGD can be broadly categorized into two approaches: (1) adaptive learning rate…

Machine Learning · Computer Science 2019-12-04 Michael R. Zhang , James Lucas , Geoffrey Hinton , Jimmy Ba

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

Since the 21st century, artificial intelligence has been leading a new round of industrial revolution. Under the training framework, the optimization algorithm aims to stably converge high-dimensional optimization to local and even global…

Machine Learning · Computer Science 2025-12-02 Meng Zhu , Quan Xiao , Weidong Min
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