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arXiv · 2406.09816

A Zeroth-Order Proximal Algorithm for Consensus Optimization

Chengan Wang·Zichong Ou·Jie Lu
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Abstract

This paper considers a consensus optimization problem, where all the nodes in a network, with access to the zeroth-order information of its local objective function only, attempt to cooperatively achieve a common minimizer of the sum of their local objectives. To address this problem, we develop ZoPro, a zeroth-order proximal algorithm, which incorporates a zeroth-order oracle for approximating Hessian and gradient into a recently proposed, high-performance distributed second-order proximal algorithm. We show that the proposed ZoPro algorithm, equipped with a dynamic stepsize, converges linearly to a neighborhood of the optimum in expectation, provided that each local objective function is strongly convex and smooth. Extensive simulations demonstrate that ZoPro converges faster than several state-of-the-art distributed zeroth-order algorithms and outperforms a few distributed second-order algorithms in terms of running time for reaching given accuracy.

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Chengan Wang, Zichong Ou, Jie Lu. 2024-06-14. A Zeroth-Order Proximal Algorithm for Consensus Optimization. https://arxiv.org/abs/2406.09816

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