Decentralized projected Riemannian stochastic recursive momentum method for nonconvex optimization

[2412.02382] Decentralized projected Riemannian stochastic recursive momentum method for nonconvex optimization Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2412.02382 (math) [Submitted on 3 Dec 2024 ( v1 ), last revised 27 Aug 2026 (this version, v3)] Title: Decentralized projected Riemannian stochastic recursive momentum method for nonconvex optimization Authors: Kangkang Deng , Jiang Hu View PDF HTML (experimental) Abstract: This paper studies decentralized optimization over a compact submanifold within a communication network of $n$ nodes, where each node possesses a smooth non-convex local cost function, and the goal is to jointly minimize the sum of these local costs. We focus particularly on the online setting, where local data is processed in real-time as it streams in, without the need for full data storage. We propose a decentralized projected Riemannian stochastic recursive momentum (DPRSRM) method that employs local hybrid stochastic gradient estimators and uses the network to track the global gradient. DPRSRM achieves an oracle complexity of \(\mathcal{O}(\epsilon^{-\frac{3}{2}})\), outperforming existing methods that have at most \(\mathcal{O}(\epsilon^{-2})\) complexity. Our method requires only $\mathcal{O}(1)$ gradient evaluations per iteration for each local node and does not require restarting with a large batch gradient. Furthermore, we demonstrate the effectiveness of our proposed methods compared to state-of-the-art ones through numerical experiments on principal component analysis problems and low-rank matrix completion. Comments: 25 Pages Subjects: Optimization and Control (math.OC) MSC classes: 90C06, 90C22, 90C26, 90C56 Cite as: arXiv:2412.02382 [math.OC] (or arXiv:2412.02382v3 [math.OC] for this version) https://doi.org/10.48550/arXiv.2412.02382 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Kangkang Deng [ view email ] [v1] Tue, 3 Dec 2024 11:07:58 UTC (468 KB) [v2] Wed, 16 Apr 2025 05:24:55 UTC (749 KB) [v3] Thu, 27 Aug 2026 00:50:07 UTC (455 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2024-12 Change to browse by: math References & Citations SciX Google Scholar Semantic Scholar export BibTeX citation Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab)

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