The Barzilai-Borwein Method for Distributed Optimization over Unbalanced Directed Networks

Fuente: arXiv
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Main Authors: Hu, Jinhui, Chen, Xin, Zheng, Lifeng, Zhang, Ling, Li, Huaqing
Format: Preprint
Published: 2023
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author Hu, Jinhui
Chen, Xin
Zheng, Lifeng
Zhang, Ling
Li, Huaqing
author_facet Hu, Jinhui
Chen, Xin
Zheng, Lifeng
Zhang, Ling
Li, Huaqing
contents This paper studies optimization problems over multi-agent systems, in which all agents cooperatively minimize a global objective function expressed as a sum of local cost functions. Each agent in the systems uses only local computation and communication in the overall process without leaking their private information. Based on the Barzilai-Borwein (BB) method and multi-consensus inner loops, a distributed algorithm with the availability of larger stepsizes and accelerated convergence, namely ADBB, is proposed. Moreover, owing to employing only row-stochastic weight matrices, ADBB can resolve the optimization problems over unbalanced directed networks without requiring the knowledge of neighbors' out-degree for each agent. Via establishing contraction relationships between the consensus error, the optimality gap, and the gradient tracking error, ADBB is theoretically proved to converge linearly to the globally optimal solution. A real-world data set is used in simulations to validate the correctness of the theoretical analysis.
format Preprint
id arxiv_https___arxiv_org_abs_2305_11469
institution arXiv
publishDate 2023
record_format arxiv
spellingShingle The Barzilai-Borwein Method for Distributed Optimization over Unbalanced Directed Networks
Hu, Jinhui
Chen, Xin
Zheng, Lifeng
Zhang, Ling
Li, Huaqing
Optimization and Control
Systems and Control
This paper studies optimization problems over multi-agent systems, in which all agents cooperatively minimize a global objective function expressed as a sum of local cost functions. Each agent in the systems uses only local computation and communication in the overall process without leaking their private information. Based on the Barzilai-Borwein (BB) method and multi-consensus inner loops, a distributed algorithm with the availability of larger stepsizes and accelerated convergence, namely ADBB, is proposed. Moreover, owing to employing only row-stochastic weight matrices, ADBB can resolve the optimization problems over unbalanced directed networks without requiring the knowledge of neighbors' out-degree for each agent. Via establishing contraction relationships between the consensus error, the optimality gap, and the gradient tracking error, ADBB is theoretically proved to converge linearly to the globally optimal solution. A real-world data set is used in simulations to validate the correctness of the theoretical analysis.
title The Barzilai-Borwein Method for Distributed Optimization over Unbalanced Directed Networks
topic Optimization and Control
Systems and Control
url https://arxiv.org/abs/2305.11469