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Stochastic Gradient Descent (SGD) stands as a cornerstone optimization algorithm with proven real-world empirical successes but relatively limited theoretical understanding. Recent research has illuminated a key factor contributing to its…

Machine Learning · Computer Science 2024-01-24 Gregory Dexter , Borja Ocejo , Sathiya Keerthi , Aman Gupta , Ayan Acharya , Rajiv Khanna

One of the most widely used methods for solving large-scale stochastic optimization problems is distributed asynchronous stochastic gradient descent (DASGD), a family of algorithms that result from parallelizing stochastic gradient descent…

Optimization and Control · Mathematics 2021-07-08 Zhengyuan Zhou , Panayotis Mertikopoulos , Nicholas Bambos , Peter W. Glynn , Yinyu Ye

Stochastic gradient descent (SGD) has been a go-to algorithm for nonconvex stochastic optimization problems arising in machine learning. Its theory however often requires a strong framework to guarantee convergence properties. We hereby…

Optimization and Control · Mathematics 2025-03-11 Azar Louzi

Decentralized optimization has emerged as a critical paradigm for distributed learning, enabling scalable training while preserving data privacy through peer-to-peer collaboration. However, existing methods often suffer from communication…

Machine Learning · Computer Science 2026-01-06 Yijie Zhou , Shi Pu

In recent years, even though Stochastic Gradient Descent (SGD) and its variants are well-known for training neural networks, it suffers from limitations such as the lack of theoretical guarantees, vanishing gradients, and excessive…

Optimization and Control · Mathematics 2022-02-17 Junxiang Wang , Hongyi Li , Liang Zhao

To reduce the long training time of large deep neural network (DNN) models, distributed synchronous stochastic gradient descent (S-SGD) is commonly used on a cluster of workers. However, the speedup brought by multiple workers is limited by…

Machine Learning · Computer Science 2020-03-03 Shaohuai Shi , Zhenheng Tang , Qiang Wang , Kaiyong Zhao , Xiaowen Chu

In order to extract the best possible performance from asynchronous stochastic gradient descent one must increase the mini-batch size and scale the learning rate accordingly. In order to achieve further speedup we introduce a technique that…

Computation and Language · Computer Science 2018-09-17 Nikolay Bogoychev , Marcin Junczys-Dowmunt , Kenneth Heafield , Alham Fikri Aji

Arguably the biggest challenge in applying neural networks is tuning the hyperparameters, in particular the learning rate. The sensitivity to the learning rate is due to the reliance on backpropagation to train the network. In this paper we…

Machine Learning · Statistics 2018-08-08 Francois Fagan , Garud Iyengar

Large-scale distributed training of deep acoustic models plays an important role in today's high-performance automatic speech recognition (ASR). In this paper we investigate a variety of asynchronous decentralized distributed training…

Computation and Language · Computer Science 2021-10-22 Xiaodong Cui , Wei Zhang , Abdullah Kayi , Mingrui Liu , Ulrich Finkler , Brian Kingsbury , George Saon , David Kung

As one of the most fundamental stochastic optimization algorithms, stochastic gradient descent (SGD) has been intensively developed and extensively applied in machine learning in the past decade. There have been some modified SGD-type…

Machine Learning · Computer Science 2022-01-28 Ruinan Jin , Yu Xing , Xingkang He

Stochastic gradient descent (SGD) with stochastic momentum is popular in nonconvex stochastic optimization and particularly for the training of deep neural networks. In standard SGD, parameters are updated by improving along the path of the…

Machine Learning · Computer Science 2021-06-08 Jun-Kun Wang , Chi-Heng Lin , Jacob Abernethy

Stochastic gradient descent (SGD) is the optimization algorithm of choice in many machine learning applications such as regularized empirical risk minimization and training deep neural networks. The classical convergence analysis of SGD is…

Optimization and Control · Mathematics 2018-07-10 Lam M. Nguyen , Phuong Ha Nguyen , Marten van Dijk , Peter Richtárik , Katya Scheinberg , Martin Takáč

We analyze asynchronous-type algorithms for distributed SGD in the heterogeneous setting, where each worker has its own computation and communication speeds, as well as data distribution. In these algorithms, workers compute possibly stale…

Machine Learning · Computer Science 2023-11-01 Rustem Islamov , Mher Safaryan , Dan Alistarh

Deep learning models are dominating almost all artificial intelligence tasks such as vision, text, and speech processing. Stochastic Gradient Descent (SGD) is the main tool for training such models, where the computations are usually…

Machine Learning · Computer Science 2023-01-10 Matteo Cacciola , Antonio Frangioni , Masoud Asgharian , Alireza Ghaffari , Vahid Partovi Nia

Bilevel optimization has been widely used in many machine learning applications such as hyperparameter optimization and meta learning. Recently, many simple stochastic gradient descent(SGD) type algorithms(without using momentum and…

Optimization and Control · Mathematics 2023-06-21 Haimei Huo , Risheng Liu , Zhixun Su

With the increase in the amount of data and the expansion of model scale, distributed parallel training becomes an important and successful technique to address the optimization challenges. Nevertheless, although distributed stochastic…

Machine Learning · Computer Science 2019-09-23 Shuheng Shen , Linli Xu , Jingchang Liu , Xianfeng Liang , Yifei Cheng

Recently many first and second order variants of SGD have been proposed to facilitate training of Deep Neural Networks (DNNs). A common limitation of these works stem from the fact that they use the same learning rate across all instances…

Machine Learning · Computer Science 2021-05-31 Shreyas Saxena , Nidhi Vyas , Dennis DeCoste

We consider a variant of the stochastic gradient descent (SGD) with a random learning rate and reveal its convergence properties. SGD is a widely used stochastic optimization algorithm in machine learning, especially deep learning. Numerous…

Machine Learning · Statistics 2025-09-09 Naoki Yoshida , Shogo Nakakita , Masaaki Imaizumi

We study the problem of stochastic optimization for deep learning in the parallel computing environment under communication constraints. A new algorithm is proposed in this setting where the communication and coordination of work among…

Machine Learning · Computer Science 2015-10-27 Sixin Zhang , Anna Choromanska , Yann LeCun

We propose a stochastic optimization method for minimizing loss functions, expressed as an expected value, that adaptively controls the batch size used in the computation of gradient approximations and the step size used to move along such…

Machine Learning · Computer Science 2020-03-04 Achraf Bahamou , Donald Goldfarb