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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2311.01317 |
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| _version_ | 1866916587137662976 |
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| author | Nguyen, Edward Duc Hien Jiang, Xin Ying, Bicheng Uribe, César A. |
| author_facet | Nguyen, Edward Duc Hien Jiang, Xin Ying, Bicheng Uribe, César A. |
| contents | This paper studies sequences of graphs satisfying the finite-time consensus property (i.e., iterating through such a finite sequence is equivalent to performing global or exact averaging) and their use in Gradient Tracking. We provide an explicit weight matrix representation of the studied sequences and prove their finite-time consensus property. Moreover, we incorporate the studied finite-time consensus topologies into Gradient Tracking and present a new algorithmic scheme called Gradient Tracking for Finite-Time Consensus Topologies (GT-FT). We analyze the new scheme for nonconvex problems with stochastic gradient estimates. Our analysis shows that the convergence rate of GT-FT does not depend on the heterogeneity of the agents' functions or the connectivity of any individual graph in the topology sequence. Furthermore, owing to the sparsity of the graphs, GT-FT requires lower communication costs than Gradient Tracking using the static counterpart of the topology sequence. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2311_01317 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On graphs with finite-time consensus and their use in gradient tracking Nguyen, Edward Duc Hien Jiang, Xin Ying, Bicheng Uribe, César A. Optimization and Control This paper studies sequences of graphs satisfying the finite-time consensus property (i.e., iterating through such a finite sequence is equivalent to performing global or exact averaging) and their use in Gradient Tracking. We provide an explicit weight matrix representation of the studied sequences and prove their finite-time consensus property. Moreover, we incorporate the studied finite-time consensus topologies into Gradient Tracking and present a new algorithmic scheme called Gradient Tracking for Finite-Time Consensus Topologies (GT-FT). We analyze the new scheme for nonconvex problems with stochastic gradient estimates. Our analysis shows that the convergence rate of GT-FT does not depend on the heterogeneity of the agents' functions or the connectivity of any individual graph in the topology sequence. Furthermore, owing to the sparsity of the graphs, GT-FT requires lower communication costs than Gradient Tracking using the static counterpart of the topology sequence. |
| title | On graphs with finite-time consensus and their use in gradient tracking |
| topic | Optimization and Control |
| url | https://arxiv.org/abs/2311.01317 |