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Heavy ball momentum is crucial in accelerating (stochastic) gradient-based optimization algorithms for machine learning. Existing heavy ball momentum is usually weighted by a uniform hyperparameter, which relies on excessive tuning.…

Machine Learning · Computer Science 2021-10-19 Tao Sun , Huaming Ling , Zuoqiang Shi , Dongsheng Li , Bao Wang

We introduce AlphaGrad, a memory-efficient, conditionally stateless optimizer addressing the memory overhead and hyperparameter complexity of adaptive methods like Adam. AlphaGrad enforces scale invariance via tensor-wise L2 gradient…

Machine Learning · Computer Science 2025-04-24 Soham Sane

Adaptive Moment Estimation (ADAM) is a very popular training algorithm for deep neural networks and belongs to the family of adaptive gradient descent optimizers. However to the best of the authors knowledge no complete convergence analysis…

Machine Learning · Computer Science 2021-02-22 Sebastian Bock , Martin Georg Weiß

Current state-of-the-art optimizers are adaptive gradient-based optimization methods such as Adam. Recently, there has been an increasing interest in formulating gradient-based optimizers in a probabilistic framework for better modeling the…

Machine Learning · Computer Science 2025-04-21 Haotian Chen , Anna Kuzina , Babak Esmaeili , Jakub M Tomczak

Adaptive gradient methods, especially Adam-type methods (such as Adam, AMSGrad, and AdaBound), have been proposed to speed up the training process with an element-wise scaling term on learning rates. However, they often generalize poorly…

Machine Learning · Computer Science 2021-07-20 Zhou Shao , Tong Lin

Communication-efficient variants of SGD, specifically local SGD, have received a great deal of interest in recent years. These approaches compute multiple gradient steps locally on each worker, before averaging model parameters, helping…

Machine Learning · Computer Science 2025-06-13 Charles-Étienne Joseph , Benjamin Thérien , Abhinav Moudgil , Boris Knyazev , Eugene Belilovsky

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

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

The Adam optimizer is a cornerstone of modern deep learning, yet the empirical necessity of each of its individual components is often taken for granted. This paper presents a focused investigation into the role of bias-correction, a…

Machine Learning · Computer Science 2025-11-27 Sam Laing , Antonio Orvieto

Adaptive gradient methods, e.g. \textsc{Adam}, have achieved tremendous success in machine learning. Scaling the learning rate element-wisely by a certain form of second moment estimate of gradients, such methods are able to attain rapid…

Machine Learning · Computer Science 2022-02-10 Yizhou Wang , Yue Kang , Can Qin , Huan Wang , Yi Xu , Yulun Zhang , Yun Fu

A major challenge in training large-scale machine learning models is configuring the training process to maximize model performance, i.e., finding the best training setup from a vast design space. In this work, we unlock a gradient-based…

Machine Learning · Statistics 2025-03-19 Logan Engstrom , Andrew Ilyas , Benjamin Chen , Axel Feldmann , William Moses , Aleksander Madry

Gradient descent based optimization methods are the methods of choice to train deep neural networks in machine learning. Beyond the standard gradient descent method, also suitable modified variants of standard gradient descent involving…

Optimization and Control · Mathematics 2025-04-29 Steffen Dereich , Arnulf Jentzen , Adrian Riekert

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

Adaptive optimizers like AdamW apply uniform hyperparameters across all parameter groups, ignoring heterogeneous optimization dynamics across layers and modules. We address this limitation by proposing MetaAdamW - a new optimizer that…

Machine Learning · Computer Science 2026-05-07 JiangBo Zhao , ZhaoXin Liu

Adaptive gradient methods have shown excellent performances for solving many machine learning problems. Although multiple adaptive gradient methods were recently studied, they mainly focus on either empirical or theoretical aspects and also…

Optimization and Control · Mathematics 2022-05-13 Feihu Huang , Junyi Li , Heng Huang

In this paper, we propose a general deep learning training framework XGrad which introduces weight prediction into the popular gradient-based optimizers to boost their convergence and generalization when training the deep neural network…

Machine Learning · Computer Science 2024-04-09 Lei Guan , Dongsheng Li , Yanqi Shi , Jian Meng

Popular approaches for minimizing loss in data-driven learning often involve an abstraction or an explicit retention of the history of gradients for efficient parameter updates. The aggregated history of gradients nudges the parameter…

Machine Learning · Computer Science 2021-06-22 Paul-Aymeric McRae , Prasanna Parthasarathi , Mahmoud Assran , Sarath Chandar

Most popular optimizers for deep learning can be broadly categorized as adaptive methods (e.g. Adam) and accelerated schemes (e.g. stochastic gradient descent (SGD) with momentum). For many models such as convolutional neural networks…

Machine Learning · Computer Science 2020-12-22 Juntang Zhuang , Tommy Tang , Yifan Ding , Sekhar Tatikonda , Nicha Dvornek , Xenophon Papademetris , James S. Duncan

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

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