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In this paper, we focus on the decentralized optimization problem over the Stiefel manifold, which is defined on a connected network of $d$ agents. The objective is an average of $d$ local functions, and each function is privately held by…

Optimization and Control · Mathematics 2022-07-13 Lei Wang , Xin Liu

The problem of optimization on Stiefel manifold, i.e., minimizing functions of (not necessarily square) matrices that satisfy orthogonality constraints, has been extensively studied. Yet, a new approach is proposed based on, for the first…

Machine Learning · Computer Science 2023-03-06 Lingkai Kong , Yuqing Wang , Molei Tao

With the prevalence of Large Learning Models (LLM), Split Federated Learning (SFL), which divides a learning model into server-side and client-side models, has emerged as an appealing technology to deal with the heavy computational burden…

Distributed, Parallel, and Cluster Computing · Computer Science 2025-01-03 Yipeng Liang , Qimei Chen , Guangxu Zhu , Muhammad Kaleem Awan , Hao Jiang

Decentralized optimization methods enable on-device training of machine learning models without a central coordinator. In many scenarios communication between devices is energy demanding and time consuming and forms the bottleneck of the…

Optimization and Control · Mathematics 2020-11-04 Dmitry Kovalev , Anastasia Koloskova , Martin Jaggi , Peter Richtarik , Sebastian U. Stich

Distributed stochastic optimization algorithms can simultaneously process large-scale datasets, significantly accelerating model training. However, their effectiveness is often hindered by the sparsity of distributed networks and data…

Machine Learning · Computer Science 2025-02-14 Yuchen Hu , Xi Chen , Weidong Liu , Xiaojun Mao

The growing demands of remote detection and increasing amount of training data make distributed machine learning under communication constraints a critical issue. This work provides a communication-efficient quantum algorithm that tackles…

Quantum Physics · Physics 2023-04-26 Hao Tang , Boning Li , Guoqing Wang , Haowei Xu , Changhao Li , Ariel Barr , Paola Cappellaro , Ju Li

Due to the high communication overhead when training machine learning models in a distributed environment, modern algorithms invariably rely on lossy communication compression. However, when untreated, the errors caused by compression…

Machine Learning · Computer Science 2023-10-31 Ilyas Fatkhullin , Alexander Tyurin , Peter Richtárik

Federated Learning (FL) enables decentralized model training across multiple clients while optionally preserving data privacy. However, communication efficiency remains a critical bottleneck, particularly for large-scale models. In this…

Machine Learning · Computer Science 2025-11-11 Arnaud Descours , Léonard Deroose , Jan Ramon

We investigate fast and communication-efficient algorithms for the classic problem of minimizing a sum of strongly convex and smooth functions that are distributed among $n$ different nodes, which can communicate using a limited number of…

Optimization and Control · Mathematics 2021-06-21 Foivos Alimisis , Peter Davies , Dan Alistarh

Bilevel optimization has been applied to a wide variety of machine learning models, and numerous stochastic bilevel optimization algorithms have been developed in recent years. However, most existing algorithms restrict their focus on the…

Machine Learning · Computer Science 2023-03-28 Hongchang Gao , Bin Gu , My T. Thai

This paper studies distributed stochastic nonconvex optimization problems with compressed communication and differential privacy, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed…

Optimization and Control · Mathematics 2026-03-24 Antai Xie , Xiaoqiang Ren , Xinlei Yi , Tao Yang , Xiaofan Wang

This paper studies the problem of distributed Riemannian optimization over a network of agents whose cost functions are geodesically smooth but possibly geodesically non-convex. Extending a well-known distributed optimization strategy…

Signal Processing · Electrical Eng. & Systems 2026-05-26 Xiuheng Wang , Ricardo Borsoi , Cédric Richard , Ali H. Sayed

Manifold learning is a central task in modern statistics and data science. Many datasets (cells, documents, images, molecules) can be represented as point clouds embedded in a high dimensional ambient space, however the degrees of freedom…

Machine Learning · Statistics 2025-02-18 Stephen Zhang , Gilles Mordant , Tetsuya Matsumoto , Geoffrey Schiebinger

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

Training at the edge utilizes continuously evolving data generated at different locations. Privacy concerns prohibit the co-location of this spatially as well as temporally distributed data, deeming it crucial to design training algorithms…

Machine Learning · Computer Science 2023-03-28 Sakshi Choudhary , Sai Aparna Aketi , Gobinda Saha , Kaushik Roy

This paper studies distributed nonconvex optimization problems with stochastic gradients for a multi-agent system, in which each agent aims to minimize the sum of all agents' cost functions by using local compressed information exchange. We…

Optimization and Control · Mathematics 2024-03-05 Antai Xie , Xinlei Yi , Xiaofan Wang , Ming Cao , Xiaoqiang Ren

Motivated by the emergence of federated learning (FL), we design and analyze federated methods for addressing: (i) Nondifferentiable nonconvex optimization; (ii) Bilevel optimization; (iii) Minimax problems; and (iv) Two-stage stochastic…

Optimization and Control · Mathematics 2025-07-04 Yuyang Qiu , Uday V. Shanbhag , Farzad Yousefian

Communication compression is essential for scalable distributed training of modern machine learning models, but it often degrades convergence due to the noise it introduces. Error Feedback (EF) mechanisms are widely adopted to mitigate this…

Optimization and Control · Mathematics 2025-11-19 Abdurakhmon Sadiev , Yury Demidovich , Igor Sokolov , Grigory Malinovsky , Sarit Khirirat , Peter Richtárik

In recent years, distributed optimization is proven to be an effective approach to accelerate training of large scale machine learning models such as deep neural networks. With the increasing computation power of GPUs, the bottleneck of…

Machine Learning · Computer Science 2021-09-14 Xiangyi Chen , Xiaoyun Li , Ping Li

In this paper, the distributed strongly convex optimization problem is studied with spatio-temporal compressed communication and equality constraints. For the case where each agent holds an distributed local equality constraint, a…

Systems and Control · Electrical Eng. & Systems 2025-03-05 Zihao Ren , Lei Wang , Zhengguang Wu , Guodong Shi