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We propose Adam-SHANG, a Lyapunov-guided Adam-type method that couples momentum, adaptive preconditioning, and a curvature-aware correction through a more stable lagged-preconditioner update. For stochastic smooth convex optimization, we…

Optimization and Control · Mathematics 2026-05-14 Yaxin Yu , Long Chen , Minfu Feng

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

Adam is a widely used optimization algorithm in deep learning, yet the specific class of objective functions where it exhibits inherent advantages remains underexplored. Unlike prior studies requiring external schedulers and $\beta_2$ near…

Machine Learning · Computer Science 2026-05-26 Zhiwei Bai , Jiajie Zhao , Zhangchen Zhou , Zhi-Qin John Xu , Yaoyu Zhang

This work proposes Alada, an adaptive momentum method for stochastic optimization over large-scale matrices. Alada employs a rank-one factorization approach to estimate the second moment of gradients, where factors are updated alternatively…

Machine Learning · Computer Science 2025-12-16 Xiaoyu He , Yu Cai , Jin Jia , Canxi Huang , Wenqing Chen , Zibin Zheng

Selecting an optimizer is a central step in the contemporary deep learning pipeline. In this paper, we demonstrate the sensitivity of optimizer comparisons to the hyperparameter tuning protocol. Our findings suggest that the hyperparameter…

Machine Learning · Computer Science 2020-06-17 Dami Choi , Christopher J. Shallue , Zachary Nado , Jaehoon Lee , Chris J. Maddison , George E. Dahl

Stochastic optimization algorithms using exponential moving averages of the past gradients, such as ADAM, RMSProp and AdaGrad, have been having great successes in many applications, especially in training deep neural networks. ADAM in…

Machine Learning · Computer Science 2026-01-30 Ruiqi Wang , Diego Klabjan

We make contributions towards improving adaptive-optimizer performance. Our improvements are based on suppression of the range of adaptive stepsizes in the AdaBelief optimizer. Firstly, we show that the particular placement of the parameter…

Machine Learning · Computer Science 2023-01-25 Guoqiang Zhang , Kenta Niwa , W. Bastiaan Kleijn

Existing convergence analyses of Q-learning mostly focus on the vanilla stochastic gradient descent (SGD) type of updates. Despite the Adaptive Moment Estimation (Adam) has been commonly used for practical Q-learning algorithms, there has…

Optimization and Control · Mathematics 2020-07-16 Bowen Weng , Huaqing Xiong , Yingbin Liang , Wei Zhang

Adaptive algorithms like AdaGrad and AMSGrad are successful in nonconvex optimization owing to their parameter-agnostic ability -- requiring no a priori knowledge about problem-specific parameters nor tuning of learning rates. However, when…

Optimization and Control · Mathematics 2022-10-17 Junchi Yang , Xiang Li , Niao He

AdamW has long been the dominant optimizer in language model pretraining, despite numerous claims that alternative optimizers offer 1.4 to 2x speedup. We posit that two methodological shortcomings have obscured fair comparisons and hindered…

Machine Learning · Computer Science 2025-09-08 Kaiyue Wen , David Hall , Tengyu Ma , Percy Liang

Large language models (LLMs) have demonstrated impressive generalization and emergent capabilities, yet their pre-training remains computationally expensive and sensitive to optimization dynamics. While Adam-based optimizers offer fast…

Machine Learning · Computer Science 2025-10-01 Junjie Wang , Pan Zhou , Yiming Dong , Huan Li , Jia Li , Xun Zhou , Qicheng Lao , Cong Fang , Zhouchen Lin

We address the challenge of optimizing meta-parameters (hyperparameters) in machine learning, a key factor for efficient training and high model performance. Rather than relying on expensive meta-parameter search methods, we introduce…

Machine Learning · Computer Science 2025-07-10 Arsalan Sharifnassab , Saber Salehkaleybar , Richard Sutton

The insufficient generalization of adaptive moment estimation (Adam) has hindered its broader application. Recent studies have shown that flat minima in loss landscapes are highly associated with improved generalization. Inspired by the…

Machine Learning · Computer Science 2024-12-18 Long Jin , Han Nong , Liangming Chen , Zhenming Su

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

We propose a stepsize adaptation scheme for stochastic gradient descent. It operates directly with the loss function and rescales the gradient in order to make fixed predicted progress on the loss. We demonstrate its capabilities by…

Machine Learning · Computer Science 2018-12-03 Michal Rolinek , Georg Martius

The spherical noise added to gradients in differentially private (DP) training undermines the performance of adaptive optimizers like AdaGrad and Adam, and hence many recent works have proposed algorithms to address this challenge. However,…

Machine Learning · Computer Science 2025-07-03 Arun Ganesh , Brendan McMahan , Abhradeep Thakurta

The performance of optimizers, particularly in deep learning, depends considerably on their chosen hyperparameter configuration. The efficacy of optimizers is often studied under near-optimal problem-specific hyperparameters, and finding…

Machine Learning · Computer Science 2020-08-18 Prabhu Teja Sivaprasad , Florian Mai , Thijs Vogels , Martin Jaggi , François Fleuret

Deep neural networks are commonly trained using stochastic non-convex optimization procedures, which are driven by gradient information estimated on fractions (batches) of the dataset. While it is commonly accepted that batch size is an…

Machine Learning · Computer Science 2016-04-26 Ilya Loshchilov , Frank Hutter

First-order optimization methods are currently the mainstream in training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by employing the diagonal matrix preconditioning of the stochastic…

Machine Learning · Computer Science 2025-03-12 Damien Martins Gomes , Yanlei Zhang , Eugene Belilovsky , Guy Wolf , Mahdi S. Hosseini

First-order optimization methods remain the standard for training deep neural networks (DNNs). Optimizers like Adam incorporate limited curvature information by preconditioning the stochastic gradient with a diagonal matrix. Despite the…

Machine Learning · Computer Science 2025-04-30 Damien Martins Gomes
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