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While significant theoretical progress has been achieved, unveiling the generalization mystery of overparameterized neural networks still remains largely elusive. In this paper, we study the generalization behavior of shallow neural…

Machine Learning · Computer Science 2022-09-21 Yunwen Lei , Rong Jin , Yiming Ying

We consider a distributed learning problem in which the computation is carried out on a system consisting of a master node and multiple worker nodes. In such systems, the existence of slow-running machines called stragglers will cause a…

Information Theory · Computer Science 2019-01-16 Shunsuke Horii , Takahiro Yoshida , Manabu Kobayashi , Toshiyasu Matsushima

We study the problem of how to distribute the training of large-scale deep learning models in the parallel computing environment. We propose a new distributed stochastic optimization method called Elastic Averaging SGD (EASGD). We analyze…

Machine Learning · Computer Science 2016-05-10 Sixin Zhang

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

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

Recently there are a considerable amount of work devoted to the study of the algorithmic stability and generalization for stochastic gradient descent (SGD). However, the existing stability analysis requires to impose restrictive assumptions…

Machine Learning · Computer Science 2020-06-16 Yunwen Lei , Yiming Ying

This paper investigates the problems large-scale distributed composite convex optimization, with motivations from a broad range of applications, including multi-agent systems, federated learning, smart grids, wireless sensor networks,…

Optimization and Control · Mathematics 2025-12-16 Maoran Wang , Xingju Cai , Yongxin Chen

We establish a data-dependent notion of algorithmic stability for Stochastic Gradient Descent (SGD), and employ it to develop novel generalization bounds. This is in contrast to previous distribution-free algorithmic stability results for…

Machine Learning · Computer Science 2018-02-19 Ilja Kuzborskij , Christoph H. Lampert

In distributed machine learning, a central node outsources computationally expensive calculations to external worker nodes. The properties of optimization procedures like stochastic gradient descent (SGD) can be leveraged to mitigate the…

Distributed, Parallel, and Cluster Computing · Computer Science 2023-04-19 Maximilian Egger , Serge Kas Hanna , Rawad Bitar

Stochastic Gradient Descent (SGD) is a workhorse in machine learning, yet its slow convergence can be a computational bottleneck. Variance reduction techniques such as SAG, SVRG and SAGA have been proposed to overcome this weakness,…

Machine Learning · Computer Science 2016-02-29 Thomas Hofmann , Aurelien Lucchi , Simon Lacoste-Julien , Brian McWilliams

Uniform stability is a notion of algorithmic stability that bounds the worst case change in the model output by the algorithm when a single data point in the dataset is replaced. An influential work of Hardt et al. (2016) provides strong…

Machine Learning · Computer Science 2020-06-15 Raef Bassily , Vitaly Feldman , Cristóbal Guzmán , Kunal Talwar

The recent advances in sensor technologies and smart devices enable the collaborative collection of a sheer volume of data from multiple information sources. As a promising tool to efficiently extract useful information from such big data,…

Machine Learning · Computer Science 2019-03-08 Richeng Jin , Xiaofan He , Huaiyu Dai

Many machine learning tasks can be formulated as a stochastic compositional optimization (SCO) problem such as reinforcement learning, AUC maximization, and meta-learning, where the objective function involves a nested composition…

Machine Learning · Computer Science 2023-11-23 Ming Yang , Xiyuan Wei , Tianbao Yang , Yiming Ying

We present an optimizer which uses Bayesian optimization to tune the system parameters of distributed stochastic gradient descent (SGD). Given a specific context, our goal is to quickly find efficient configurations which appropriately…

Machine Learning · Statistics 2016-12-04 Valentin Dalibard , Michael Schaarschmidt , Eiko Yoneki

We consider speeding up stochastic gradient descent (SGD) by parallelizing it across multiple workers. We assume the same data set is shared among $N$ workers, who can take SGD steps and coordinate with a central server. While it is…

Distributed, Parallel, and Cluster Computing · Computer Science 2021-10-28 Artin Spiridonoff , Alex Olshevsky , Ioannis Ch. Paschalidis

The stochastic gradient descent (SGD) algorithm is the algorithm we use to train neural networks. However, it remains poorly understood how the SGD navigates the highly nonlinear and degenerate loss landscape of a neural network. In this…

Machine Learning · Computer Science 2025-06-13 Liu Ziyin , Hongchao Li , Masahito Ueda

The success of deep learning has led to a rising interest in the generalization property of the stochastic gradient descent (SGD) method, and stability is one popular approach to study it. Existing works based on stability have studied…

Machine Learning · Statistics 2019-03-08 Yi Zhou , Yingbin Liang , Huishuai Zhang

The distributed subgradient method (DSG) is a widely discussed algorithm to cope with large-scale distributed optimization problems in the arising machine learning applications. Most exisiting works on DSG focus on ideal communication…

Signal Processing · Electrical Eng. & Systems 2022-08-24 Zhaoyue Xia , Jun Du , Yong Ren

Asynchronous stochastic gradient methods are central to scalable distributed optimization, particularly when devices differ in computational capabilities. Such settings arise naturally in federated learning, where training takes place on…

Optimization and Control · Mathematics 2026-02-20 Artavazd Maranjyan , Peter Richtárik

In the era of big data, optimizing large scale machine learning problems becomes a challenging task and draws significant attention. Asynchronous optimization algorithms come out as a promising solution. Recently, decoupled asynchronous…

Machine Learning · Computer Science 2016-09-30 Zhouyuan Huo , Bin Gu , Heng Huang