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Volume 8 Issue 8
Aug.  2021

IEEE/CAA Journal of Automatica Sinica

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Xiaoxing Ren, Dewei Li, Yugeng Xi and Haibin Shao, "Distributed Subgradient Algorithm for Multi-Agent Optimization With Dynamic Stepsize," IEEE/CAA J. Autom. Sinica, vol. 8, no. 8, pp. 1451-1464, Aug. 2021. doi: 10.1109/JAS.2021.1003904
Citation: Xiaoxing Ren, Dewei Li, Yugeng Xi and Haibin Shao, "Distributed Subgradient Algorithm for Multi-Agent Optimization With Dynamic Stepsize," IEEE/CAA J. Autom. Sinica, vol. 8, no. 8, pp. 1451-1464, Aug. 2021. doi: 10.1109/JAS.2021.1003904

Distributed Subgradient Algorithm for Multi-Agent Optimization With Dynamic Stepsize

doi: 10.1109/JAS.2021.1003904
Funds:  This work was supported by the Key Research and Development Project in Guangdong Province (2020B0101050001), the National Science Foundation of China (61973214, 61590924, 61963030), the Natural Science Foundation of Shanghai (19ZR1476200). Part of this work has been presented in the 16th International Conference on Control & Automation, Oct. 9–11, 2020 (Virtual) Sapporo, Hokkaido, Japan. This paper also includes the asynchronous case, more theoretical and numerical results compared to the conference paper
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  • In this paper, we consider distributed convex optimization problems on multi-agent networks. We develop and analyze the distributed gradient method which allows each agent to compute its dynamic stepsize by utilizing the time-varying estimate of the local function value at the global optimal solution. Our approach can be applied to both synchronous and asynchronous communication protocols. Specifically, we propose the distributed subgradient with uncoordinated dynamic stepsizes (DS-UD) algorithm for synchronous protocol and the AsynDGD algorithm for asynchronous protocol. Theoretical analysis shows that the proposed algorithms guarantee that all agents reach a consensus on the solution to the multi-agent optimization problem. Moreover, the proposed approach with dynamic stepsizes eliminates the requirement of diminishing stepsize in existing works. Numerical examples of distributed estimation in sensor networks are provided to illustrate the effectiveness of the proposed approach.

     

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    Highlights

    • This paper proposes a novel dynamic stepsize selection approach for the distributed gradient algorithm and develops the associated distributed gradient algorithms for synchronous and asynchronous gossip-like communication protocol.
    • Differently from the existing distributed algorithms whose diminishing or fixed stepsizes are determined before the algorithm is run, the proposed algorithms use dynamic stepsizes that rely on the time-varying estimates of the optimal function values generated at each iteration during the algorithms.
    • On the one hand, the dynamic stepsize needs no knowledge of the global information on the network or the objective functions, which makes the proposed algorithms more applicable compared to distributed algorithms with fixed stepsizes. On the other hand, the dynamic stepsize can overcome inefficient computations caused by the diminishing stepsize and the proposed algorithms can achieve faster convergence than distributed algorithms with diminishing stepsizes.

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