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Adaptive Moment Estimation (Adam) is a cornerstone optimization algorithm in deep learning, widely recognized for its flexibility with adaptive learning rates and efficiency in handling large-scale data. However, despite its practical…

Machine Learning · Computer Science 2025-05-21 Ruinan Jin , Xiao Li , Yaoliang Yu , Baoxiang Wang

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

Many popular first-order optimization methods (e.g., Momentum, AdaGrad, Adam) accelerate the convergence rate of deep learning models. However, these algorithms require auxiliary parameters, which cost additional memory proportional to the…

Machine Learning · Computer Science 2019-02-27 Ryan Spring , Anastasios Kyrillidis , Vijai Mohan , Anshumali Shrivastava

In this paper, we present CT-AGD (Curvature-Tuned Accelerated Gradient Descent), an optimization method for non-convex optimization problems in deep learning training tasks. CT-AGD is a general boosting procedure that accelerates…

Machine Learning · Computer Science 2026-05-18 Manuel Graca , L. Miguel Silveira , Arlindo Oliveira , Frank Liu

Adaptive gradient methods, which adopt historical gradient information to automatically adjust the learning rate, despite the nice property of fast convergence, have been observed to generalize worse than stochastic gradient descent (SGD)…

Machine Learning · Computer Science 2020-06-24 Jinghui Chen , Dongruo Zhou , Yiqi Tang , Ziyan Yang , Yuan Cao , Quanquan Gu

Decentralized training of deep neural networks has attracted significant attention for its theoretically superior scalability over synchronous data-parallel methods like All-Reduce. However, realizing this potential in multi-node training…

Distributed, Parallel, and Cluster Computing · Computer Science 2024-10-17 Zesen Wang , Jiaojiao Zhang , Xuyang Wu , Mikael Johansson

Deep learning algorithms - typically consisting of a class of deep neural networks trained by a stochastic gradient descent (SGD) optimization method - are nowadays the key ingredients in many artificial intelligence (AI) systems and have…

Machine Learning · Computer Science 2024-07-12 Steffen Dereich , Robin Graeber , Arnulf Jentzen

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

Recent years have witnessed a clear trend towards language models with an ever-increasing number of parameters, as well as the growing training overhead and memory usage. Distributed training, particularly through Sharded Data Parallelism…

Machine Learning · Computer Science 2024-11-26 Jinda Jia , Cong Xie , Hanlin Lu , Daoce Wang , Hao Feng , Chengming Zhang , Baixi Sun , Haibin Lin , Zhi Zhang , Xin Liu , Dingwen Tao

As foundation models continue to scale, pretraining increasingly relies on data-parallel distributed optimization, making bandwidth-limited gradient synchronization a key bottleneck. Orthogonally, projection-based low-rank optimizers were…

Machine Learning · Computer Science 2026-02-10 Sizhe Dang , Jiaqi Shao , Xiaodong Zheng , Guang Dai , Yan Song , Haishan Ye

Adaptive gradient methods (AGMs) have become popular in optimizing the nonconvex problems in deep learning area. We revisit AGMs and identify that the adaptive learning rate (A-LR) used by AGMs varies significantly across the dimensions of…

Machine Learning · Computer Science 2019-09-12 Qianqian Tong , Guannan Liang , Jinbo Bi

Compressed Stochastic Gradient Descent (SGD) algorithms have been recently proposed to address the communication bottleneck in distributed and decentralized optimization problems, such as those that arise in federated machine learning.…

Machine Learning · Statistics 2022-07-21 Adarsh M. Subramaniam , Akshayaa Magesh , Venugopal V. Veeravalli

SignSGD compresses each stochastic gradient coordinate to a single bit, offering substantial memory and communication savings, but its 1-bit quantization removes magnitude information and is known to leave a generalization gap relative to…

Machine Learning · Computer Science 2026-04-29 Haoran Chen , Wentao Wang

Due to the high communication cost in distributed and federated learning problems, methods relying on compression of communicated messages are becoming increasingly popular. While in other contexts the best performing gradient-type methods…

Optimization and Control · Mathematics 2020-06-29 Zhize Li , Dmitry Kovalev , Xun Qian , Peter Richtárik

We study distributed adaptive algorithms with local updates (intermittent communication). Despite the great empirical success of adaptive methods in distributed training of modern machine learning models, the theoretical benefits of local…

Machine Learning · Computer Science 2025-02-13 Ziheng Cheng , Margalit Glasgow

Adaptive moment estimation (Adam), as a Stochastic Gradient Descent (SGD) variant, has gained widespread popularity in federated learning (FL) due to its fast convergence. However, federated Adam (FedAdam) algorithms suffer from a threefold…

Machine Learning · Computer Science 2025-09-22 Xiumei Deng , Jun Li , Kang Wei , Long Shi , Zehui Xiong , Ming Ding , Wen Chen , Shi Jin , H. Vincent Poor

Stochastic gradient descent (SGD) is the main approach for training deep networks: it moves towards the optimum of the cost function by iteratively updating the parameters of a model in the direction of the gradient of the loss evaluated on…

Machine Learning · Computer Science 2021-03-30 Loris Nanni , Gianluca Maguolo , Alessandra Lumini

Adam is known to perform significantly better than Stochastic Gradient Descent (SGD) in language models, a phenomenon for which a number of explanations have been proposed. In this work, we revisit this "optimizer gap" through a series of…

Machine Learning · Computer Science 2025-06-17 Teodora Srećković , Jonas Geiping , Antonio Orvieto

When scaling distributed training, the communication overhead is often the bottleneck. In this paper, we propose a novel SGD variant with reduced communication and adaptive learning rates. We prove the convergence of the proposed algorithm…

Machine Learning · Computer Science 2020-12-08 Cong Xie , Oluwasanmi Koyejo , Indranil Gupta , Haibin Lin

Mini-batch stochastic gradient descent (SGD) is state of the art in large scale distributed training. The scheme can reach a linear speedup with respect to the number of workers, but this is rarely seen in practice as the scheme often…

Optimization and Control · Mathematics 2019-05-06 Sebastian U. Stich