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

Lei Qin; Ye Pu

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arXiv · 2508.06922

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

Lei Qin·Ye Pu

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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.

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BibTeX RIS

Lei Qin, Ye Pu. 2025-08-09. On the Convergence of a Noisy Gradient Method for Non-convex Distributed Resource Allocation: Saddle Point Escape. https://arxiv.org/abs/2508.06922

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