On the Convergence of a Noisy Gradient Method for Non-convex Distributed Resource Allocation: Saddle Point Escape

[2508.06922] On the Convergence of a Noisy Gradient Method for Non-convex Distributed Resource Allocation: Saddle Point Escape Skip to main content Search Submit Donate Log in Mathematics > Optimization and Control arXiv:2508.06922 (math) [Submitted on 9 Aug 2025 ( v1 ), last revised 25 Aug 2026 (this version, v2)] Title: On the Convergence of a Noisy Gradient Method for Non-convex Distributed Resource Allocation: Saddle Point Escape Authors: Lei Qin , Ye Pu View PDF HTML (experimental) Abstract: This paper considers a class of distributed resource allocation problems where each agent privately holds a smooth, potentially non-convex local objective, subject to a globally coupled equality constraint. Built upon the existing method, Laplacian-weighted Gradient Descent, we propose to add random perturbations to the gradient iteration to enable efficient escape from saddle points and achieve second-order convergence guarantees. We show that, with a sufficiently small fixed step size, the iterates of all agents reach an approximate second-order stationary point with high probability. Numerical experiments confirm the effectiveness of the proposed approach, demonstrating improved performance over standard weighted gradient descent in non-convex scenarios. Subjects: Optimization and Control (math.OC) Cite as: arXiv:2508.06922 [math.OC] (or arXiv:2508.06922v2 [math.OC] for this version) https://doi.org/10.48550/arXiv.2508.06922 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Lei Qin [ view email ] [v1] Sat, 9 Aug 2025 10:25:36 UTC (295 KB) [v2] Tue, 25 Aug 2026 06:27:09 UTC (352 KB) Full-text links: Access Paper: View PDF HTML (experimental) TeX Source view license Current browse context: math.OC < prev | next > new | recent | 2025-08 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)

Related documents

• On the Convergence of a Noisy Gradient Method for Non-convex Distributed Resource Allocation: Saddle Point Escape#670365
• Efficient Gradient Methods for Distributed Saddle Problems#200445
• Convergence Analysis of an Inexact Proximal Trust-Region Method#1062673
• Projection-Free Algorithms for Nonsmooth Stochastic Convex-Concave Saddle-Point Problems#1129869
• Convex Optimization Is Free When Accuracy Is Expensive#1130006