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We propose a general framework for distributed stochastic optimization under delayed gradient models. In this setting, $n$ local agents leverage their own data and computation to assist a central server in minimizing a global objective…

Optimization and Control · Mathematics 2026-03-04 Xinran Zheng , Tara Javidi , Behrouz Touri

In centralized, distributed, and federated learning with stochastic gradients and $n$ workers, it was recently shown that it is infeasible to find an $\varepsilon$-stationary point faster than $\tilde{\Omega}\left(\min\left\{\frac{d \kappa…

Optimization and Control · Mathematics 2026-05-11 Grigory Begunov , Alexander Tyurin

Communication is a major bottleneck in distributed learning, especially in large-scale settings and in federated learning environments with slow links. Three standard ways to reduce this cost are communication compression, local training,…

Machine Learning · Computer Science 2026-05-21 Yassine Maziane , Ammar Mahran , Artavazd Maranjyan , Peter Richtárik

The distributed nonconvex optimization problem of minimizing a global cost function formed by a sum of $n$ local cost functions by using local information exchange is considered. This problem is an important component of many machine…

Optimization and Control · Mathematics 2022-01-11 Xinlei Yi , Shengjun Zhang , Tao Yang , Tianyou Chai , Karl H. Johansson

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

We study distributed stochastic gradient (D-SG) method and its accelerated variant (D-ASG) for solving decentralized strongly convex stochastic optimization problems where the objective function is distributed over several computational…

Optimization and Control · Mathematics 2021-10-05 Alireza Fallah , Mert Gurbuzbalaban , Asuman Ozdaglar , Umut Simsekli , Lingjiong Zhu

Distributed learning algorithms, such as the ones employed in Federated Learning (FL), require communication compression to reduce the cost of client uploads. The compression methods used in practice are often biased, making error feedback…

Machine Learning · Computer Science 2025-09-12 Tomas Ortega , Chun-Yin Huang , Xiaoxiao Li , Hamid Jafarkhani

Large neural network models present a hefty communication challenge to distributed Stochastic Gradient Descent (SGD), with a communication complexity of O(n) per worker for a model of n parameters. Many sparsification and quantization…

Machine Learning · Computer Science 2020-06-17 Subhadeep Bhattacharya , Weikuan Yu , Fahim Tahmid Chowdhury

We investigate the Randomized Stochastic Accelerated Gradient (RSAG) method, utilizing either constant or adaptive step sizes, for stochastic optimization problems with generalized smooth objective functions. Under relaxed affine variance…

Optimization and Control · Mathematics 2025-02-25 Chenhao Yu , Yusu Hong , Junhong Lin

We first propose a decentralized proximal stochastic gradient tracking method (DProxSGT) for nonconvex stochastic composite problems, with data heterogeneously distributed on multiple workers in a decentralized connected network. To save…

Optimization and Control · Mathematics 2023-03-01 Yonggui Yan , Jie Chen , Pin-Yu Chen , Xiaodong Cui , Songtao Lu , Yangyang Xu

Decentralized training has been actively studied in recent years. Although a wide variety of methods have been proposed, yet the decentralized momentum SGD method is still underexplored. In this paper, we propose a novel periodic…

Machine Learning · Computer Science 2020-08-25 Hongchang Gao , Heng Huang

Gradient quantization is an emerging technique in reducing communication costs in distributed learning. Existing gradient quantization algorithms often rely on engineering heuristics or empirical observations, lacking a systematic approach…

Machine Learning · Computer Science 2021-08-02 Guangfeng Yan , Shao-Lun Huang , Tian Lan , Linqi Song

Asynchronous stochastic gradient descent (SGD) enables scalable distributed training but suffers from gradient staleness. Existing mitigation strategies, such as delay-adaptive learning rates and staleness-aware filtering, typically…

Machine Learning · Computer Science 2026-05-15 Tehila Dahan , Roie Reshef , Sharon Goldstein , Kfir Y. Levy

Distributed Stochastic Gradient Descent (SGD) when run in a synchronous manner, suffers from delays in runtime as it waits for the slowest workers (stragglers). Asynchronous methods can alleviate stragglers, but cause gradient staleness…

Machine Learning · Statistics 2020-03-25 Sanghamitra Dutta , Jianyu Wang , Gauri Joshi

In distributed machine learning, efficient training across multiple agents with different data distributions poses significant challenges. Even with a centralized coordinator, current algorithms that achieve optimal communication complexity…

Machine Learning · Computer Science 2024-08-13 Junchi Yang , Murat Yildirim , Qiu Feng

The stochastic gradient descent (SGD) optimization algorithm plays a central role in a series of machine learning applications. The scientific literature provides a vast amount of upper error bounds for the SGD method. Much less attention…

Numerical Analysis · Mathematics 2020-10-05 Arnulf Jentzen , Philippe von Wurstemberger

Distributed optimization plays an important role in modern large-scale machine learning and data processing systems by optimizing the utilization of computational resources. One of the classical and popular approaches is Local Stochastic…

Optimization and Control · Mathematics 2024-12-19 Andrey Sadchikov , Savelii Chezhegov , Aleksandr Beznosikov , Alexander Gasnikov

Lossy gradient compression, with either unbiased or biased compressors, has become a key tool to avoid the communication bottleneck in centrally coordinated distributed training of machine learning models. We analyze the performance of two…

Machine Learning · Computer Science 2020-12-23 Sebastian U. Stich

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

This paper targets solving distributed machine learning problems such as federated learning in a communication-efficient fashion. A class of new stochastic gradient descent (SGD) approaches have been developed, which can be viewed as the…

Optimization and Control · Mathematics 2020-02-27 Tianyi Chen , Yuejiao Sun , Wotao Yin
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