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Stochastic gradient descent (SGD) is one of the most widely used optimization methods for parallel and distributed processing of large datasets. One of the key limitations of distributed SGD is the need to regularly communicate the…

最优化与控制 · 数学 2018-10-25 Xiaojian Xu , Ulugbek S. Kamilov

Normalization techniques are a boon for modern deep learning. They let weights converge more quickly with often better generalization performances. It has been argued that the normalization-induced scale invariance among the weights…

机器学习 · 计算机科学 2021-01-19 Byeongho Heo , Sanghyuk Chun , Seong Joon Oh , Dongyoon Han , Sangdoo Yun , Gyuwan Kim , Youngjung Uh , Jung-Woo Ha

Large language models (LLMs) have demonstrated remarkable performance due to their large parameter counts and extensive training data. However, their scale leads to significant memory bottlenecks during training, especially when using…

机器学习 · 计算机科学 2026-05-14 Ziqing Wen , Jiahuan Wang , Ping Luo , Dongsheng Li , Tao Sun

The dynamic behavior of RMSprop and Adam algorithms is studied through a combination of careful numerical experiments and theoretical explanations. Three types of qualitative features are observed in the training loss curve: fast initial…

机器学习 · 计算机科学 2021-10-01 Chao Ma , Lei Wu , Weinan E

In federated learning, communication cost is often a critical bottleneck to scale up distributed optimization algorithms to collaboratively learn a model from millions of devices with potentially unreliable or limited communication and…

机器学习 · 计算机科学 2020-11-24 Farzin Haddadpour , Mohammad Mahdi Kamani , Aryan Mokhtari , Mehrdad Mahdavi

In this paper, we propose and analyze SQuARM-SGD, a communication-efficient algorithm for decentralized training of large-scale machine learning models over a network. In SQuARM-SGD, each node performs a fixed number of local SGD steps…

机器学习 · 计算机科学 2021-10-12 Navjot Singh , Deepesh Data , Jemin George , Suhas Diggavi

Local SGD is a promising approach to overcome the communication overhead in distributed learning by reducing the synchronization frequency among worker nodes. Despite the recent theoretical advances of local SGD in empirical risk…

机器学习 · 计算机科学 2021-03-01 Yuyang Deng , Mehrdad Mahdavi

The best performing Binary Neural Networks (BNNs) are usually attained using Adam optimization and its multi-step training variants. However, to the best of our knowledge, few studies explore the fundamental reasons why Adam is superior to…

机器学习 · 计算机科学 2021-06-22 Zechun Liu , Zhiqiang Shen , Shichao Li , Koen Helwegen , Dong Huang , Kwang-Ting Cheng

Local stochastic gradient descent (Local-SGD), also referred to as federated averaging, is an approach to distributed optimization where each device performs more than one SGD update per communication. This work presents an empirical study…

Running out of GPU memory has become a main bottleneck for large-scale DNN training. How to reduce the memory footprint during training has received intensive research attention. We find that previous gradient accumulation reduces…

机器学习 · 计算机科学 2023-06-01 Yijia Zhang , Yibo Han , Shijie Cao , Guohao Dai , Youshan Miao , Ting Cao , Fan Yang , Ningyi Xu

With the rapid development of natural language processing technology, large-scale language models (LLM) have achieved remarkable results in a variety of tasks. However, how to effectively train these huge models and improve their…

人工智能 · 计算机科学 2024-12-09 Jiajing Chen , Bingying Liu , Xiaoxuan Liao , Jia Gao , Hongye Zheng , Yue Li

This paper provides the first tight convergence analyses for RMSProp and Adam in non-convex optimization under the most relaxed assumptions of coordinate-wise generalized smoothness and affine noise variance. We first analyze RMSProp, which…

机器学习 · 统计学 2025-03-11 Qi Zhang , Yi Zhou , Shaofeng Zou

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…

最优化与控制 · 数学 2024-08-01 Steffen Dereich , Arnulf Jentzen

Large language models (LLMs) such as ChatGPT have evolved into powerful and ubiquitous tools. Fine-tuning on small datasets allows LLMs to acquire specialized skills for specific tasks efficiently. Although LLMs provide great utility in…

机器学习 · 计算机科学 2025-10-08 Ruoxing Yang

We provide a simple proof of convergence covering both the Adam and Adagrad adaptive optimization algorithms when applied to smooth (possibly non-convex) objective functions with bounded gradients. We show that in expectation, the squared…

机器学习 · 统计学 2022-10-18 Alexandre Défossez , Léon Bottou , Francis Bach , Nicolas Usunier

Despite the wide applications of Adam in reinforcement learning (RL), the theoretical convergence of Adam-type RL algorithms has not been established. This paper provides the first such convergence analysis for two fundamental RL algorithms…

机器学习 · 计算机科学 2020-08-18 Huaqing Xiong , Tengyu Xu , Yingbin Liang , Wei Zhang

For SGD based distributed stochastic optimization, computation complexity, measured by the convergence rate in terms of the number of stochastic gradient calls, and communication complexity, measured by the number of inter-node…

最优化与控制 · 数学 2019-05-14 Hao Yu , Rong Jin

Massive amounts of data have led to the training of large-scale machine learning models on a single worker inefficient. Distributed machine learning methods such as Parallel-SGD have received significant interest as a solution to tackle…

机器学习 · 计算机科学 2022-03-31 S Vineeth

While stochastic gradient descent (SGD) is still the most popular optimization algorithm in deep learning, adaptive algorithms such as Adam have established empirical advantages over SGD in some deep learning applications such as training…

机器学习 · 计算机科学 2023-06-02 Yan Pan , Yuanzhi Li

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,…

最优化与控制 · 数学 2024-06-21 Steffen Dereich , Arnulf Jentzen , Adrian Riekert