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We propose an adaptive step size with an energy approach for a suitable class of preconditioned gradient descent methods. We focus on settings where the preconditioning is applied to address the constraints in optimization problems, such as…

最优化与控制 · 数学 2024-06-17 Hailiang Liu , Levon Nurbekyan , Xuping Tian , Yunan Yang

The history of meta-learning methods based on gradient descent is reviewed, focusing primarily on methods that adapt step-size (learning rate) meta-parameters.

机器学习 · 计算机科学 2022-02-22 Richard S. Sutton

Stochastic gradient descent method and its variants constitute the core optimization algorithms that achieve good convergence rates for solving machine learning problems. These rates are obtained especially when these algorithms are…

机器学习 · 计算机科学 2024-03-14 S. Ilker Birbil , Ozgur Martin , Gonenc Onay , Figen Oztoprak

Stochastic gradient descent (SGD) is a popular algorithm for optimization problems arising in high-dimensional inference tasks. Here one produces an estimator of an unknown parameter from independent samples of data by iteratively…

机器学习 · 统计学 2023-06-23 Gerard Ben Arous , Reza Gheissari , Aukosh Jagannath

Training deep neural networks with Stochastic Gradient Descent, or its variants, requires careful choice of both learning rate and batch size. While smaller batch sizes generally converge in fewer training epochs, larger batch sizes offer…

机器学习 · 计算机科学 2018-02-15 Aditya Devarakonda , Maxim Naumov , Michael Garland

Stochastic gradient descent is the method of choice for large-scale machine learning problems, by virtue of its light complexity per iteration. However, it lags behind its non-stochastic counterparts with respect to the convergence rate,…

机器学习 · 统计学 2016-03-23 Vatsal Shah , Megasthenis Asteris , Anastasios Kyrillidis , Sujay Sanghavi

In stochastic optimization, a common tool to deal sequentially with large sample is to consider the well-known stochastic gradient algorithm. Nevertheless, since the stepsequence is the same for each direction, this can lead to bad results…

最优化与控制 · 数学 2023-03-03 Antoine Godichon-Baggioni , Pierre Tarrago

Several variants of stochastic gradient descent (SGD) have been proposed to improve the learning effectiveness and efficiency when training deep neural networks, among which some recent influential attempts would like to adaptively control…

机器学习 · 计算机科学 2020-10-22 Jie Liu , Chen Lin , Chuming Li , Lu Sheng , Ming Sun , Junjie Yan , Wanli Ouyang

In this paper, we describe a stochastic adaptive fast gradient descent method based on the mirror variant of similar triangles method. To our knowledge, this is the first attempt to use adaptivity in stochastic method. Additionally, a main…

最优化与控制 · 数学 2017-12-04 Alexander Tyurin

We present a theoretical analysis of stochastic optimization methods in terms of their sensitivity with respect to the step size. We identify a key quantity that, for each method, describes how the performance degrades as the step size…

最优化与控制 · 数学 2026-05-27 Fabian Schaipp , Robert M. Gower , Adrien Taylor

Stochastic gradient descent updates parameters with summation gradient computed from a random data batch. This summation will lead to unbalanced training process if the data we obtained is unbalanced. To address this issue, this paper takes…

机器学习 · 计算机科学 2019-05-22 Tao Yi , Xingxuan Wang

Many iterative procedures in stochastic optimization exhibit a transient phase followed by a stationary phase. During the transient phase the procedure converges towards a region of interest, and during the stationary phase the procedure…

机器学习 · 统计学 2018-02-26 Jerry Chee , Panos Toulis

In reinforcement learning (RL), offline learning decoupled learning from data collection and is useful in dealing with exploration-exploitation tradeoff and enables data reuse in many applications. In this work, we study two offline…

机器学习 · 计算机科学 2022-02-08 Jing Dong , Xin T. Tong

Stochastic gradient descent (SGD) type optimization schemes are fundamental ingredients in a large number of machine learning based algorithms. In particular, SGD type optimization schemes are frequently employed in applications involving…

数值分析 · 数学 2020-07-22 Aritz Bercher , Lukas Gonon , Arnulf Jentzen , Diyora Salimova

Stochastic gradient descent (SGD) provides a simple and efficient way to solve a broad range of machine learning problems. Here, we focus on distribution regression (DR), involving two stages of sampling: Firstly, we regress from…

机器学习 · 统计学 2021-03-08 Nicole Mücke

Stochastic Gradient Descent (SGD) methods see many uses in optimization problems. Modifications to the algorithm, such as momentum-based SGD methods have been known to produce better results in certain cases. Much of this, however, is due…

机器学习 · 计算机科学 2025-04-22 Eric Lu

Stochastic Gradient Descent (SGD) and its variants are the most used algorithms in machine learning applications. In particular, SGD with adaptive learning rates and momentum is the industry standard to train deep networks. Despite the…

机器学习 · 统计学 2020-07-29 Xiaoyu Li , Francesco Orabona

Asynchronous stochastic gradient descent (ASGD) is a standard way to exploit heterogeneous compute resources in distributed learning: instead of forcing fast workers to wait for slow ones, the server updates the model whenever a gradient…

机器学习 · 计算机科学 2026-05-14 Ammar Mahran , Artavazd Maranjyan , Peter Richtárik

Stochastic Gradient Descent (SGD) is very useful in optimization problems with high-dimensional non-convex target functions, and hence constitutes an important component of several Machine Learning and Data Analytics methods. Recently there…

分布式、并行与集群计算 · 计算机科学 2019-11-11 Karl Bäckström , Marina Papatriantafilou , Philippas Tsigas

Although stochastic gradient descent (SGD) method and its variants (e.g., stochastic momentum methods, AdaGrad) are the choice of algorithms for solving non-convex problems (especially deep learning), there still remain big gaps between the…

最优化与控制 · 数学 2019-03-07 Zaiyi Chen , Zhuoning Yuan , Jinfeng Yi , Bowen Zhou , Enhong Chen , Tianbao Yang