PMGT-VR: a Decentralized Proximal-gradient Algorithmic Framework with Variance Reduction
This paper considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic framework, called PMGT-VR, which combines several techniques, including multi-consensus, gradient tracking, and variance reduction. The proposed fr...
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| Vydáno v: | IEEE transactions on pattern analysis and machine intelligence Ročník 48; číslo 1; s. 1 - 12 |
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| Médium: | Journal Article |
| Jazyk: | angličtina |
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United States
IEEE
05.09.2025
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| ISSN: | 0162-8828, 1939-3539, 2160-9292, 1939-3539 |
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| Abstract | This paper considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic framework, called PMGT-VR, which combines several techniques, including multi-consensus, gradient tracking, and variance reduction. The proposed framework imitates centralized algorithms and algorithms under this framework achieve convergence rates similar to that of their centralized counterparts. We also describe and analyze two representative algorithms, PMGT-SAGA and PMGT-LSVRG, and compare them to existing state-of-the-art proximal algorithms. To the best of our knowledge, PMGT-VR is the first linearly convergent decentralized stochastic algorithm that can solve decentralized composite optimization problems. Numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms. |
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| AbstractList | This article considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic framework, called PMGT-VR, which combines several techniques, including multi-consensus, gradient tracking, and variance reduction. The proposed framework imitates centralized algorithms and algorithms under this framework achieve convergence rates similar to that of their centralized counterparts. We also describe and analyze two representative algorithms, PMGT-SAGA and PMGT-LSVRG, and compare them to existing state-of-the-art proximal algorithms. To the best of our knowledge, PMGT-VR is the first linearly convergent decentralized stochastic algorithm that can solve decentralized composite optimization problems. Numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms. This paper considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic framework, called PMGT-VR, which combines several techniques, including multi-consensus, gradient tracking, and variance reduction. The proposed framework imitates centralized algorithms and algorithms under this framework achieve convergence rates similar to that of their centralized counterparts. We also describe and analyze two representative algorithms, PMGT-SAGA and PMGT-LSVRG, and compare them to existing state-of-the-art proximal algorithms. To the best of our knowledge, PMGT-VR is the first linearly convergent decentralized stochastic algorithm that can solve decentralized composite optimization problems. Numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms.This paper considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic framework, called PMGT-VR, which combines several techniques, including multi-consensus, gradient tracking, and variance reduction. The proposed framework imitates centralized algorithms and algorithms under this framework achieve convergence rates similar to that of their centralized counterparts. We also describe and analyze two representative algorithms, PMGT-SAGA and PMGT-LSVRG, and compare them to existing state-of-the-art proximal algorithms. To the best of our knowledge, PMGT-VR is the first linearly convergent decentralized stochastic algorithm that can solve decentralized composite optimization problems. Numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms. This paper considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic framework, called PMGT-VR, which combines several techniques, including multi-consensus, gradient tracking, and variance reduction. The proposed framework imitates centralized algorithms and algorithms under this framework achieve convergence rates similar to that of their centralized counterparts. We also describe and analyze two representative algorithms, PMGT-SAGA and PMGT-LSVRG, and compare them to existing state-of-the-art proximal algorithms. To the best of our knowledge, PMGT-VR is the first linearly convergent decentralized stochastic algorithm that can solve decentralized composite optimization problems. Numerical experiments are provided to demonstrate the effectiveness of the proposed algorithms. |
| Author | Ye, Haishan Zhang, Tong Xiong, Wei |
| Author_xml | – sequence: 1 givenname: Haishan surname: Ye fullname: Ye, Haishan email: hsye_cs@outlook.com organization: Shenzhen Research Institute of Big Data, The Chinese University of Hong Kong, Shenzhen, China – sequence: 2 givenname: Wei surname: Xiong fullname: Xiong, Wei email: weixiong5237@gmail.com organization: The Hong Kong University of Science and Technology, China – sequence: 3 givenname: Tong surname: Zhang fullname: Zhang, Tong email: tongzhang@tongzhang-ml.org organization: The Hong Kong University of Science and Technology, China |
| BackLink | https://www.ncbi.nlm.nih.gov/pubmed/40911449$$D View this record in MEDLINE/PubMed |
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| Snippet | This paper considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic... This article considers the decentralized composite optimization problem. We propose a novel decentralized variance-reduction proximal-gradient algorithmic... |
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| SubjectTerms | Complexity theory Convergence Decentralized optimization Loss measurement Network topology Optimization proximal-gradient Servers Symmetric matrices Topology Training variance reduction Vectors |
| Title | PMGT-VR: a Decentralized Proximal-gradient Algorithmic Framework with Variance Reduction |
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