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The performance of stochastic gradient descent (SGD) depends critically on how learning rates are tuned and decreased over time. We propose a method to automatically adjust multiple learning rates so as to minimize the expected error at any…

机器学习 · 统计学 2013-02-19 Tom Schaul , Sixin Zhang , Yann LeCun

Stochastic gradient algorithms are the main focus of large-scale optimization problems and led to important successes in the recent advancement of the deep learning algorithms. The convergence of SGD depends on the careful choice of…

机器学习 · 计算机科学 2017-03-03 Caglar Gulcehre , Jose Sotelo , Marcin Moczulski , Yoshua Bengio

Stochastic gradient algorithms have been the main focus of large-scale learning problems and they led to important successes in machine learning. The convergence of SGD depends on the careful choice of learning rate and the amount of the…

机器学习 · 计算机科学 2015-11-03 Caglar Gulcehre , Marcin Moczulski , Yoshua Bengio

Recent work has established an empirically successful framework for adapting learning rates for stochastic gradient descent (SGD). This effectively removes all needs for tuning, while automatically reducing learning rates over time on…

机器学习 · 计算机科学 2013-03-28 Tom Schaul , Yann LeCun

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

We introduce a novel algorithm for gradient-based optimization of stochastic objective functions. The method may be seen as a variant of SGD with momentum equipped with an adaptive learning rate automatically adjusted by an 'energy'…

最优化与控制 · 数学 2022-03-24 Hailiang Liu , Xuping Tian

State-of-the-art training algorithms for deep learning models are based on stochastic gradient descent (SGD). Recently, many variations have been explored: perturbing parameters for better accuracy (such as in Extragradient), limiting SGD…

机器学习 · 计算机科学 2022-03-23 Amirkeivan Mohtashami , Martin Jaggi , Sebastian U. Stich

Learning rate adaptation is a popular topic in machine learning. Gradient Descent trains neural nerwork with a fixed learning rate. Learning rate adaptation is proposed to accelerate the training process through adjusting the step size in…

机器学习 · 计算机科学 2022-10-20 Bozhou Chen , Hongzhi Wang , Chenmin Ba

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)…

机器学习 · 计算机科学 2020-06-24 Jinghui Chen , Dongruo Zhou , Yiqi Tang , Ziyan Yang , Yuan Cao , Quanquan Gu

Stochastic gradient descent (SGD) is a standard optimization method to minimize a training error with respect to network parameters in modern neural network learning. However, it typically suffers from proliferation of saddle points in the…

机器学习 · 计算机科学 2017-11-23 Haiping Huang , Taro Toyoizumi

We propose a Stochastic Gradient Descent (SGD)-type algorithm for Personalized Federated Learning which can be particularly attractive for mobile energy-limited regimes due to its low per-client computational cost. The model to be trained…

机器学习 · 计算机科学 2025-12-15 Sotirios Nikoloutsopoulos , Iordanis Koutsopoulos , Michalis K. Titsias

While machine learning has achieved remarkable results in a wide variety of domains, the training of models often requires large datasets that may need to be collected from different individuals. As sensitive information may be contained in…

机器学习 · 计算机科学 2023-02-07 Richeng Jin , Xiaofan He , Huaiyu Dai

The performance of gradient-based optimization methods, such as standard gradient descent (GD), greatly depends on the choice of learning rate. However, it can require a non-trivial amount of user tuning effort to select an appropriate…

机器学习 · 计算机科学 2025-10-14 Nikola Surjanovic , Alexandre Bouchard-Côté , Trevor Campbell

We study adaptive methods for differentially private convex optimization, proposing and analyzing differentially private variants of a Stochastic Gradient Descent (SGD) algorithm with adaptive stepsizes, as well as the AdaGrad algorithm. We…

机器学习 · 计算机科学 2021-06-28 Hilal Asi , John Duchi , Alireza Fallah , Omid Javidbakht , Kunal Talwar

Stochastic gradient descent (SGD) algorithm and its variations have been effectively used to optimize neural network models. However, with the rapid growth of big data and deep learning, SGD is no longer the most suitable choice due to its…

机器学习 · 计算机科学 2024-02-13 Anuraganand Sharma

We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by…

机器学习 · 计算机科学 2018-08-23 Atilim Gunes Baydin , Robert Cornish , David Martinez Rubio , Mark Schmidt , Frank Wood

The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…

数值分析 · 数学 2020-10-05 Arnulf Jentzen , Philippe von Wurstemberger

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…

机器学习 · 计算机科学 2021-03-30 Loris Nanni , Gianluca Maguolo , Alessandra Lumini

The learning rate is an important tuning parameter for stochastic gradient descent (SGD) and can greatly influence its performance. However, appropriate selection of a learning rate schedule across all iterations typically requires a…

机器学习 · 计算机科学 2025-05-29 Nikola Surjanovic , Alexandre Bouchard-Côté , Trevor Campbell

Momentum plays a crucial role in stochastic gradient-based optimization algorithms for accelerating or improving training deep neural networks (DNNs). In deep learning practice, the momentum is usually weighted by a well-calibrated…

机器学习 · 计算机科学 2020-12-04 Bao Wang , Qiang Ye
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