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In deep learning, different kinds of deep networks typically need different optimizers, which have to be chosen after multiple trials, making the training process inefficient. To relieve this issue and consistently improve the model…

Machine Learning · Computer Science 2024-12-02 Xingyu Xie , Pan Zhou , Huan Li , Zhouchen Lin , Shuicheng Yan

Adam is widely recognized as one of the most effective optimizers for training deep neural networks (DNNs). Despite its remarkable empirical success, its theoretical convergence analysis remains unsatisfactory. Existing works predominantly…

Machine Learning · Computer Science 2025-07-10 Hanyang Peng , Shuang Qin , Yue Yu , Fangqing Jiang , Hui Wang , Zhouchen Lin

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

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 propose a continuous-time scheme for large-scale optimization that introduces individual, adaptive momentum coefficients regulated by the kinetic energy of each model parameter. This approach automatically adjusts to local landscape…

Machine Learning · Computer Science 2026-02-03 Aikaterini Karoni , Rajit Rajpal , Benedict Leimkuhler , Gabriel Stoltz

We propose AdaMuon, a novel optimizer that combines element-wise adaptivity with orthogonal updates for large-scale neural network training. AdaMuon incorporates two tightly coupled mechanisms: (1) an element-wise second momentum estimator…

Machine Learning · Computer Science 2025-12-25 Chongjie Si , Debing Zhang , Wei Shen

Time-series forecasting often faces challenges from non-stationarity, particularly distributional drift, where the data distribution evolves over time. This dynamic behavior can undermine the effectiveness of adaptive optimizers, such as…

Machine Learning · Computer Science 2026-03-12 Yuze Dong , Jinsong Wu

Min-max saddle point games have recently been intensely studied, due to their wide range of applications, including training Generative Adversarial Networks (GANs). However, most of the recent efforts for solving them are limited to special…

Optimization and Control · Mathematics 2021-08-10 Babak Barazandeh , Tianjian Huang , George Michailidis

We develop an online gradient algorithm for optimizing the performance of product-form networks through online adjustment of control parameters. The use of standard algorithms for finding optimal parameter settings is hampered by the…

Optimization and Control · Mathematics 2012-08-31 Jaron Sanders , Sem C. Borst , Johan S. H. van Leeuwaarden

Optimizer is an essential component for the success of deep learning, which guides the neural network to update the parameters according to the loss on the training set. SGD and Adam are two classical and effective optimizers on which…

Machine Learning · Computer Science 2023-07-04 Yineng Chen , Zuchao Li , Lefei Zhang , Bo Du , Hai Zhao

Neural network training can be accelerated when a learnable update rule is used in lieu of classic adaptive optimizers (e.g. Adam). However, learnable update rules can be costly and unstable to train and use. Recently, Jang et al. (2023)…

Machine Learning · Computer Science 2025-03-03 Boris Knyazev , Abhinav Moudgil , Guillaume Lajoie , Eugene Belilovsky , Simon Lacoste-Julien

This study proposes NIRMAL (Novel Integrated Robust Multi-Adaptation Learning), a novel optimization algorithm that combines multiple strategies inspired by the movements of the chess piece. These strategies include gradient descent,…

Information Retrieval · Computer Science 2025-08-07 Nirmal Gaud , Surej Mouli , Preeti Katiyar , Vaduguru Venkata Ramya

The paper presents the formulation, implementation, and evaluation of the ArcGD optimiser. The evaluation is conducted initially on a non-convex benchmark function and subsequently on a real-world ML dataset. The initial comparative study…

Machine Learning · Computer Science 2026-03-25 Nikhil Verma , Joonas Linnosmaa , Leonardo Espinosa-Leal , Napat Vajragupta

As machine learning models grow increasingly complex and computationally demanding, understanding the environmental impact of training decisions becomes critical for sustainable AI development. This paper presents a comprehensive empirical…

Machine Learning · Computer Science 2025-09-18 Tom Almog

Modern optimization algorithms that incorporate momentum and adaptive step-size offer improved performance in numerous challenging deep learning tasks. However, their effectiveness is often highly sensitive to the choice of hyperparameters,…

Machine Learning · Computer Science 2025-08-22 Rustem Islamov , Niccolo Ajroldi , Antonio Orvieto , Aurelien Lucchi

The pursuit of long-term autonomy mandates that machine learning models must continuously adapt to their changing environments and learn to solve new tasks. Continual learning seeks to overcome the challenge of catastrophic forgetting,…

Machine Learning · Computer Science 2024-07-25 Jack Foster , Alexandra Brintrup

Adaptive gradient methods such as Adam have gained increasing popularity in deep learning optimization. However, it has been observed that compared with (stochastic) gradient descent, Adam can converge to a different solution with a…

Machine Learning · Computer Science 2021-08-26 Difan Zou , Yuan Cao , Yuanzhi Li , Quanquan Gu

We introduce MVN-Grad (Momentum on Variance-Normalized Gradients), an Adam-style optimizer that improves stability and performance by combining two complementary ideas: variance-based normalization and momentum applied after normalization.…

Machine Learning · Computer Science 2026-02-12 Francisco Patitucci , Aryan Mokhtari

In the training of large language models (LLMs), updating parameters more efficiently and stably has always been an important challenge. To achieve efficient parameter updates, existing methods usually achieve performance comparable to full…

Machine Learning · Computer Science 2025-02-06 Da Chang , Yu Li , Ganzhao Yuan

Optimization algorithms with momentum, e.g., (ADAM), have been widely used for building deep learning models due to the faster convergence rates compared with stochastic gradient descent (SGD). Momentum helps accelerate SGD in the relevant…

Machine Learning · Computer Science 2020-01-24 Jiyang Bai , Yuxiang Ren , Jiawei Zhang