{"ID":2850293,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2510.22270","arxiv_id":"2510.22270","title":"Distributed Stochastic Proximal Algorithm on Riemannian Submanifolds for Weakly-convex Functions","abstract":"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.","short_abstract":"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 Rieman...","url_abs":"https://arxiv.org/abs/2510.22270","url_pdf":"https://arxiv.org/pdf/2510.22270v1","authors":"[\"Jishu Zhao\",\"Xi Wang\",\"Jinlong Lei\",\"Shixiang Chen\"]","published":"2025-10-25T12:26:25Z","proceeding":"math.OC","tasks":"[\"math.OC\",\"eess.SY\"]","methods":"[]","has_code":false}