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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2510.22270 |
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| _version_ | 1866908611961159680 |
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| author | Zhao, Jishu Wang, Xi Lei, Jinlong Chen, Shixiang |
| author_facet | Zhao, Jishu Wang, Xi Lei, Jinlong Chen, Shixiang |
| contents | This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed Riemannian stochastic proximal algorithm framework by utilizing the retraction and Riemannian consensus protocol, and analyze three specific algorithms: the distributed Riemannian stochastic subgradient, proximal point, and prox-linear algorithms. When the local costs are weakly-convex and the initial points satisfy certain conditions, we show that the iterates generated by this framework converge to a nearly stationary point in expectation while achieving consensus. We further establish the convergence rate of the algorithm framework as $\mathcal{O}(\frac{1+κ_g}{\sqrt{k}})$ where $k$ denotes the number of iterations and $κ_g$ shows the impact of manifold geometry on the algorithm performance. Finally, numerical experiments are implemented to demonstrate the theoretical results and show the empirical performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_22270 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Distributed Stochastic Proximal Algorithm on Riemannian Submanifolds for Weakly-convex Functions Zhao, Jishu Wang, Xi Lei, Jinlong Chen, Shixiang Optimization and Control Systems and Control This paper aims to investigate the distributed stochastic optimization problems on compact embedded submanifolds (in the Euclidean space) for multi-agent network systems. To address the manifold structure, we propose a distributed Riemannian stochastic proximal algorithm framework by utilizing the retraction and Riemannian consensus protocol, and analyze three specific algorithms: the distributed Riemannian stochastic subgradient, proximal point, and prox-linear algorithms. When the local costs are weakly-convex and the initial points satisfy certain conditions, we show that the iterates generated by this framework converge to a nearly stationary point in expectation while achieving consensus. We further establish the convergence rate of the algorithm framework as $\mathcal{O}(\frac{1+κ_g}{\sqrt{k}})$ where $k$ denotes the number of iterations and $κ_g$ shows the impact of manifold geometry on the algorithm performance. Finally, numerical experiments are implemented to demonstrate the theoretical results and show the empirical performance. |
| title | Distributed Stochastic Proximal Algorithm on Riemannian Submanifolds for Weakly-convex Functions |
| topic | Optimization and Control Systems and Control |
| url | https://arxiv.org/abs/2510.22270 |