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Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a…

最优化与控制 · 数学 2018-09-13 Tao Sun , Yuejiao Sun , Wotao Yin

This paper introduces a coordinate descent version of the V\~u-Condat algorithm. By coordinate descent, we mean that only a subset of the coordinates of the primal and dual iterates is updated at each iteration, the other coordinates being…

最优化与控制 · 数学 2019-01-17 Olivier Fercoq , Pascal Bianchi

In this work, we propose new adaptive step size strategies that improve several stochastic gradient methods. Our first method (StoPS) is based on the classical Polyak step size (Polyak, 1987) and is an extension of the recent development of…

机器学习 · 计算机科学 2022-08-11 Samuel Horváth , Konstantin Mishchenko , Peter Richtárik

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

Online learning algorithms are fast, memory-efficient, easy to implement, and applicable to many prediction problems, including classification, regression, and ranking. Several online algorithms were proposed in the past few decades, some…

机器学习 · 计算机科学 2015-07-03 Francesco Orabona , Koby Crammer , Nicolò Cesa-Bianchi

We study online inference and asymptotic covariance estimation for the stochastic gradient descent (SGD) algorithm. While classical methods (such as plug-in and batch-means estimators) are available, they either require inaccessible…

机器学习 · 统计学 2026-04-24 Ziyang Wei , Wanrong Zhu , Jingyang Lyu , Wei Biao Wu

This paper explores numerical methods for solving a convex differentiable semi-infinite program. We introduce a primal-dual gradient method which performs three updates iteratively: a momentum gradient ascend step to update the constraint…

最优化与控制 · 数学 2024-07-23 Yao Yao , Qihang Lin , Tianbao Yang

This paper introduces an iterative algorithm for training nonparametric additive models that enjoys favorable memory storage and computational requirements. The algorithm can be viewed as the functional counterpart of stochastic gradient…

机器学习 · 统计学 2026-01-01 Xin Chen , Jason M. Klusowski

We introduce MADGRAD, a novel optimization method in the family of AdaGrad adaptive gradient methods. MADGRAD shows excellent performance on deep learning optimization problems from multiple fields, including classification and…

机器学习 · 计算机科学 2021-08-27 Aaron Defazio , Samy Jelassi

The choice of step-size used in Stochastic Gradient Descent (SGD) optimization is empirically selected in most training procedures. Moreover, the use of scheduled learning techniques such as Step-Decaying, Cyclical-Learning, and Warmup to…

机器学习 · 计算机科学 2020-06-12 Mahdi S. Hosseini , Konstantinos N. Plataniotis

Subgradient methods are the natural extension to the non-smooth case of the classical gradient descent for regular convex optimization problems. However, in general, they are characterized by slow convergence rates, and they require…

最优化与控制 · 数学 2023-11-20 Alessandro Scagliotti , Piero Colli Franzone

We study optimization algorithms based on variance reduction for stochastic gradient descent (SGD). Remarkable recent progress has been made in this direction through development of algorithms like SAG, SVRG, SAGA. These algorithms have…

机器学习 · 计算机科学 2016-01-26 Sashank J. Reddi , Ahmed Hefny , Suvrit Sra , Barnabás Póczos , Alex Smola

With the rapid development of data collection and aggregation technologies in many scientific disciplines, it is becoming increasingly ubiquitous to conduct large-scale or online regression to analyze real-world data and unveil real-world…

统计方法学 · 统计学 2021-03-22 Jinfeng Xu , Zhiliang Ying , Na Zhao

Mirror Descent (MD) is a well-known method of solving non-smooth convex optimization problems. This paper analyzes the stochastic variant of MD with adaptive stepsizes. Its convergence on average is shown to be faster than with the fixed…

最优化与控制 · 数学 2017-05-08 Anastasia Bayandina

Large-scale optimization problems require algorithms both effective and efficient. One such popular and proven algorithm is Stochastic Gradient Descent which uses first-order gradient information to solve these problems. This paper studies…

最优化与控制 · 数学 2021-11-11 Theodoros Mamalis , Dusan Stipanovic , Petros Voulgaris

In this paper, we explore techniques centered around periodic sampling of model weights that provide convergence improvements on gradient update methods (vanilla \acs{SGD}, Momentum, Adam) for a variety of vision problems (classification,…

机器学习 · 计算机科学 2020-03-23 Samarth Tripathi , Jiayi Liu , Unmesh Kurup , Mohak Shah , Sauptik Dhar

The adaptive gradient online learning method known as AdaGrad has seen widespread use in the machine learning community in stochastic and adversarial online learning problems and more recently in deep learning methods. The method's…

机器学习 · 计算机科学 2016-10-05 Nishant A. Mehta , Alistair Rendell , Anish Varghese , Christfried Webers

Asynchronous stochastic gradient descent (ASGD) is a popular parallel optimization algorithm in machine learning. Most theoretical analysis on ASGD take a discrete view and prove upper bounds for their convergence rates. However, the…

机器学习 · 统计学 2018-05-09 Li He , Qi Meng , Wei Chen , Zhi-Ming Ma , Tie-Yan Liu

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

It has been observed in a variety of contexts that gradient descent methods have great success in solving low-rank matrix factorization problems, despite the relevant problem formulation being non-convex. We tackle a particular instance of…

数值分析 · 计算机科学 2016-06-28 Dejiao Zhang , Laura Balzano