A Zeroth-Order Proximal Algorithm for Consensus Optimization
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866914834280349696 |
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| author | Wang, Chengan Ou, Zichong Lu, Jie |
| author_facet | Wang, Chengan Ou, Zichong Lu, Jie |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_09816 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | A Zeroth-Order Proximal Algorithm for Consensus Optimization Wang, Chengan Ou, Zichong Lu, Jie Optimization and Control Multiagent Systems 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. |
| title | A Zeroth-Order Proximal Algorithm for Consensus Optimization |
| topic | Optimization and Control Multiagent Systems |
| url | https://arxiv.org/abs/2406.09816 |