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In this paper, we design two compressed decentralized algorithms for solving nonconvex stochastic optimization under two different scenarios. Both algorithms adopt a momentum technique to achieve fast convergence and a message-compression…

Machine Learning · Computer Science 2025-08-08 Wei Liu , Anweshit Panda , Ujwal Pandey , Christopher Brissette , Yikang Shen , George M. Slota , Naigang Wang , Jie Chen , Yangyang Xu

Establishing a fast rate of convergence for optimization methods is crucial to their applicability in practice. With the increasing popularity of deep learning over the past decade, stochastic gradient descent and its adaptive variants…

Optimization and Control · Mathematics 2022-01-03 Adityanarayanan Radhakrishnan , Mikhail Belkin , Caroline Uhler

In machine learning, stochastic gradient descent (SGD) is widely deployed to train models using highly non-convex objectives with equally complex noise models. Unfortunately, SGD theory often makes restrictive assumptions that fail to…

Machine Learning · Computer Science 2022-10-11 Vivak Patel , Shushu Zhang , Bowen Tian

We present two stochastic descent algorithms that apply to unconstrained optimization and are particularly efficient when the objective function is slow to evaluate and gradients are not easily obtained, as in some PDE-constrained…

Optimization and Control · Mathematics 2019-04-30 David Kozak , Stephen Becker , Alireza Doostan , Luis Tenorio

Two major momentum-based techniques that have achieved tremendous success in optimization are Polyak's heavy ball method and Nesterov's accelerated gradient. A crucial step in all momentum-based methods is the choice of the momentum…

Machine Learning · Statistics 2017-12-21 Vishwak Srinivasan , Adepu Ravi Sankar , Vineeth N Balasubramanian

We propose in this paper a new minimization algorithm based on a slightly modified version of the scalar auxiliary variable (SAV) approach coupled with a relaxation step and an adaptive strategy. It enjoys several distinct advantages over…

Numerical Analysis · Mathematics 2023-05-11 Xinyu Liu , Jie Shen , Xiaongxiong Zhang

In this paper we propose stochastic gradient-free methods and accelerated methods with momentum for solving stochastic optimization problems. All these methods rely on stochastic directions rather than stochastic gradients. We analyze the…

Optimization and Control · Mathematics 2020-01-15 Xiaopeng Luo , Xin Xu

A framework previously introduced in [3] for solving a sequence of stochastic optimization problems with bounded changes in the minimizers is extended and applied to machine learning problems such as regression and classification. The…

Machine Learning · Computer Science 2019-04-08 Craig Wilson , Yuheng Bu , Venugopal Veeravalli

In this paper, we propose a generic and simple strategy for utilizing stochastic gradient information in optimization. The technique essentially contains two consecutive steps in each iteration: 1) computing and normalizing each block…

Machine Learning · Computer Science 2018-04-24 Adams Wei Yu , Lei Huang , Qihang Lin , Ruslan Salakhutdinov , Jaime Carbonell

In this paper we demonstrate a simple heuristic adaptive restart technique that can dramatically improve the convergence rate of accelerated gradient schemes. The analysis of the technique relies on the observation that these schemes…

Optimization and Control · Mathematics 2012-04-19 Brendan O'Donoghue , Emmanuel Candes

Stochastic gradient descent (SGD) with constant momentum and its variants such as Adam are the optimization algorithms of choice for training deep neural networks (DNNs). Since DNN training is incredibly computationally expensive, there is…

Machine Learning · Computer Science 2020-04-28 Bao Wang , Tan M. Nguyen , Andrea L. Bertozzi , Richard G. Baraniuk , Stanley J. Osher

Two algorithms are proposed, analyzed, and tested for solving continuous optimization problems with nonlinear equality constraints. Each is an extension of a stochastic momentum-based method from the unconstrained setting to the setting of…

Optimization and Control · Mathematics 2026-01-21 Qi Wang , Christian Piermarini , Yunlang Zhu , Frank E. Curtis

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…

Machine Learning · Computer Science 2022-02-08 Jing Dong , Xin T. Tong

Although adaptive optimization algorithms such as Adam show fast convergence in many machine learning tasks, this paper identifies a problem of Adam by analyzing its performance in a simple non-convex synthetic problem, showing that Adam's…

Machine Learning · Computer Science 2020-05-06 Wenjie Li , Zhaoyang Zhang , Xinjiang Wang , Ping Luo

We present a novel method for convex unconstrained optimization that, without any modifications, ensures: (i) accelerated convergence rate for smooth objectives, (ii) standard convergence rate in the general (non-smooth) setting, and (iii)…

Machine Learning · Computer Science 2018-09-11 Kfir Y. Levy , Alp Yurtsever , Volkan Cevher

Stochastic gradient descent with momentum (SGDM) is one of the most widely used optimization algorithms in machine learning. While optimization properties of SGDM have been extensively studied in the literature, it remains insufficiently…

Machine Learning · Computer Science 2026-05-28 Yunwen Lei , Zimeng Wang , Xiaoming Yuan

Adaptive gradient optimizers (AdaGrad), which dynamically adjust the learning rate based on iterative gradients, have emerged as powerful tools in deep learning. These adaptive methods have significantly succeeded in various deep learning…

Optimization and Control · Mathematics 2024-12-31 Ruinan Jin , Xiaoyu Wang , Baoxiang Wang

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…

Machine Learning · Computer Science 2022-08-11 Samuel Horváth , Konstantin Mishchenko , Peter Richtárik

Adaptive gradient methods (AGMs) have become popular in optimizing the nonconvex problems in deep learning area. We revisit AGMs and identify that the adaptive learning rate (A-LR) used by AGMs varies significantly across the dimensions of…

Machine Learning · Computer Science 2019-09-12 Qianqian Tong , Guannan Liang , Jinbo Bi

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…

Optimization and Control · Mathematics 2024-08-01 Steffen Dereich , Arnulf Jentzen