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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…

最优化与控制 · 数学 2025-09-24 Steffen Dereich , Robin Graeber , Arnulf Jentzen , Adrian Riekert

Decentralized stochastic optimization has emerged as a fundamental paradigm for large-scale machine learning. However, practical implementations often rely on biased gradient estimators arising from communication compression or inexact…

最优化与控制 · 数学 2026-04-10 Qing Xu , Yiwei Liao , Wenqi Fan , Xingxing You , Songyi Dian

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

The training of modern deep learning neural network calls for large amounts of computation, which is often provided by GPUs or other specific accelerators. To scale out to achieve faster training speed, two update algorithms are mainly…

机器学习 · 计算机科学 2020-05-15 Yemao Xu , Dezun Dong , Weixia Xu , Xiangke Liao

Stochastic-gradient-based optimization has been a core enabling methodology in applications to large-scale problems in machine learning and related areas. Despite the progress, the gap between theory and practice remains significant, with…

最优化与控制 · 数学 2021-01-01 Lihua Lei , Michael I. Jordan

Adaptive gradient approaches that automatically adjust the learning rate on a per-feature basis have been very popular for training deep networks. This rich class of algorithms includes Adagrad, RMSprop, Adam, and recent extensions. All…

机器学习 · 计算机科学 2019-05-28 Jihun Yun , Aurelie C. Lozano , Eunho Yang

We introduce LDAdam, a memory-efficient optimizer for training large models, that performs adaptive optimization steps within lower dimensional subspaces, while consistently exploring the full parameter space during training. This strategy…

机器学习 · 计算机科学 2025-03-04 Thomas Robert , Mher Safaryan , Ionut-Vlad Modoranu , Dan Alistarh

Low-rank pre-training and fine-tuning have recently emerged as promising techniques for reducing the computational and storage costs of large neural networks. Training low-rank parameterizations typically relies on conventional optimizers…

机器学习 · 计算机科学 2025-10-31 Steffen Schotthöfer , Timon Klein , Jonas Kusch

The training of modern machine learning models often consists in solving high-dimensional non-convex optimisation problems that are subject to large-scale data. In this context, momentum-based stochastic optimisation algorithms have become…

最优化与控制 · 数学 2024-11-06 Kexin Jin , Jonas Latz , Chenguang Liu , Alessandro Scagliotti

Gradient descent-based optimization methods underpin the parameter training of neural networks, and hence comprise a significant component in the impressive test results found in a number of applications. Introducing stochasticity is key to…

机器学习 · 计算机科学 2021-06-01 Nikola B. Kovachki , Andrew M. Stuart

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…

机器学习 · 计算机科学 2024-12-02 Xingyu Xie , Pan Zhou , Huan Li , Zhouchen Lin , Shuicheng Yan

In many real-world applications of Machine Learning it is of paramount importance not only to provide accurate predictions, but also to ensure certain levels of robustness. Adversarial Training is a training procedure aiming at providing…

机器学习 · 计算机科学 2019-10-09 Matteo Terzi , Gian Antonio Susto , Pratik Chaudhari

Asynchronous stochastic gradient descent (SGD) enables scalable distributed training but suffers from gradient staleness. Existing mitigation strategies, such as delay-adaptive learning rates and staleness-aware filtering, typically…

机器学习 · 计算机科学 2026-05-15 Tehila Dahan , Roie Reshef , Sharon Goldstein , Kfir Y. Levy

In this paper, we consider a general stochastic optimization problem which is often at the core of supervised learning, such as deep learning and linear classification. We consider a standard stochastic gradient descent (SGD) method with a…

机器学习 · 统计学 2018-12-27 Lam M. Nguyen , Nam H. Nguyen , Dzung T. Phan , Jayant R. Kalagnanam , Katya Scheinberg

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…

机器学习 · 计算机科学 2021-02-22 Sebastian Bock , Martin Georg Weiß

Training deep reinforcement learning (RL) agents necessitates overcoming the highly unstable nonconvex stochastic optimization inherent in the trial-and-error mechanism. To tackle this challenge, we propose a physics-inspired optimization…

机器学习 · 计算机科学 2024-12-10 Yao Lyu , Xiangteng Zhang , Shengbo Eben Li , Jingliang Duan , Letian Tao , Qing Xu , Lei He , Keqiang Li

Optimization algorithms are core methods by which machine learning models iteratively minimize loss functions, update parameters, learn from data, and improve performance. Momentum SGD and AdamW represent two important optimization…

机器学习 · 计算机科学 2026-05-21 Meng Zhu , Quan Xiao , Weidong Min

Training deep neural networks is a highly nontrivial task, involving carefully selecting appropriate training algorithms, scheduling step sizes and tuning other hyperparameters. Trying different combinations can be quite labor-intensive and…

机器学习 · 计算机科学 2017-06-13 Kaifeng Lv , Shunhua Jiang , Jian Li

The goal of this paper is to accelerate the training of machine learning models, a critical challenge since the training of large-scale deep neural models can be computationally expensive. Stochastic gradient descent (SGD) and its variants…

机器学习 · 计算机科学 2025-09-22 Yuen Chen , Yian Wang , Hari Sundaram

SGD with momentum is one of the key components for improving the performance of neural networks. For decentralized learning, a straightforward approach using momentum is Distributed SGD (DSGD) with momentum (DSGDm). However, DSGDm performs…

机器学习 · 计算机科学 2023-09-26 Yuki Takezawa , Han Bao , Kenta Niwa , Ryoma Sato , Makoto Yamada