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Distributed Optimization over General Directed Networks with Random Sleep Scheme

Abstract

Distributed optimization aims at optimizing a global objective function which is described by a sum of local objective functions through local information processing and sharing. This paper studies the problem of distributed optimization over a network in which underlying graph is generally directed strongly connected. Most existing distributed algorithms require each agent to observe the gradient of the local objective function per iteration, which leads to heavy computational cost. A computation-efficient distributed optimization algorithm incorporating random sleep scheme is proposed by incorporating rescaling gradient technique to address the unbalancedness of the directed graph. The implementation of the proposed algorithm allows agents not only locally allocates the weights on the received information, but also independently decides whether to execute gradient observation at each iteration. Theoretical analysis verifies that the proposed algorithm is able to seek the optimal solution with probability one. Simulations are shown to demonstrate effectiveness of the proposed algorithm, show correctness of the theoretical analysis, and investigate the tradeoffs between convergence performance and computation cost.

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Correspondence to Lifeng Zheng or Huaqing Li.

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Publisher’s Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Recommended by Associate Editor Wei He under the direction of Editor Fuchun Sun. The work described in this paper was supported in part by the Fundamental Research Funds for the Central Universities under Grant XDJK2019AC001, in part by the Innovation Support Program for Chongqing Overseas Returnees under Grant cx2019005, and in part by the National Natural Science Foundation of China under Grant 61773321, Grant 61673080.

Zheng Wang received his B.E. degree in Electronic Information Science and Technology from University of Jinan, China, in 2015, and an M.E. degree in Electronics and Communication Engineering from Southwest University, China, in 2018. His research interests include multi-agent systems and distributed optimization.

Lifeng Zheng Lifeng Zheng received his B.E. degree in internet of things engineering from Chongqing Three Gorges University, Chongqing, China, in 2017. He is currently working toward a master’s degree in the College of Electronic and Information Engineering, Southwest University, Chongqing, China. His research interests include networked system and distributed computing.

Huaqing Li received his B.S. degree in Information and Computing Science from Chongqing University of Posts and Telecommunications, in 2009, and a Ph.D. degree in Computer Science and Technology from Chongqing University in 2013. He was a Postdoctoral Researcher at School of Electrical and Information Engineering, The University of Sydney from Sept. 2014 to Sept. 2015, and at School of Electrical and Electronic Engineering, Nanyang Technological University from Nov. 2015 to Nov. 2016. From Jul. 2018, he has been a professor at College of Electronic and Information Engineering, Southwest University. His main research interests include nonlinear dynamics and control, multi-agent systems, and distributed optimization. He serves as a Regional Editor for Neural Computing & Applications and an Editorial Board Member for IEEE Access

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Wang, Z., Zheng, L. & Li, H. Distributed Optimization over General Directed Networks with Random Sleep Scheme. Int. J. Control Autom. Syst. 18, 2534–2542 (2020). https://doi.org/10.1007/s12555-018-9543-9

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Keywords

  • Distributed convex optimization
  • multi-agent systems
  • random sleep scheme
  • row-stochastic matrix