A Zeroth-Order Proximal Algorithm for Consensus Optimization
<|reference_start|>A Zeroth-Order Proximal Algorithm for Consensus Optimization: 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.<|reference_end|>
@article{wang2024a,
    title={A Zeroth-Order Proximal Algorithm for Consensus Optimization},
    author={Chengan Wang, Zichong Ou and Jie Lu},
    journal={arXiv preprint arXiv:2406.09816},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.09816},
    primaryClass={math.OC cs.MA}
}