{"ID":2884355,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2508.06922","arxiv_id":"2508.06922","title":"On the Convergence of a Noisy Gradient Method for Non-convex Distributed Resource Allocation: Saddle Point Escape","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 converge to an approximate second-order optimal solution with high probability. Numerical experiments confirm the effectiveness of the proposed approach, demonstrating improved performance over standard weighted gradient descent in non-convex scenarios.","short_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 th...","url_abs":"https://arxiv.org/abs/2508.06922","url_pdf":"https://arxiv.org/pdf/2508.06922v1","authors":"[\"Lei Qin\",\"Ye Pu\"]","published":"2025-08-09T10:25:36Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}