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Volume 10 Issue 3
Mar.  2023

IEEE/CAA Journal of Automatica Sinica

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Article Contents
J. Hou, X. Zeng, G. Wang, J. Sun, and  J. Chen,  “Distributed momentum-based Frank-Wolfe algorithm for stochastic optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 685–699, Mar. 2023. doi: 10.1109/JAS.2022.105923
Citation: J. Hou, X. Zeng, G. Wang, J. Sun, and  J. Chen,  “Distributed momentum-based Frank-Wolfe algorithm for stochastic optimization,” IEEE/CAA J. Autom. Sinica, vol. 10, no. 3, pp. 685–699, Mar. 2023. doi: 10.1109/JAS.2022.105923

Distributed Momentum-Based Frank-Wolfe Algorithm for Stochastic Optimization

doi: 10.1109/JAS.2022.105923
Funds:  This work was supported in part by the National Key R&D Program of China (2021YFB1714800), the National Natural Science Foundation of China (62222303, 62073035, 62173034, 61925303, 62088101, 61873033), the CAAI-Huawei MindSpore Open Fund, and the Chongqing Natural Science Foundation (2021ZX4100027)
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  • This paper considers distributed stochastic optimization, in which a number of agents cooperate to optimize a global objective function through local computations and information exchanges with neighbors over a network. Stochastic optimization problems are usually tackled by variants of projected stochastic gradient descent. However, projecting a point onto a feasible set is often expensive. The Frank-Wolfe (FW) method has well-documented merits in handling convex constraints, but existing stochastic FW algorithms are basically developed for centralized settings. In this context, the present work puts forth a distributed stochastic Frank-Wolfe solver, by judiciously combining Nesterov’s momentum and gradient tracking techniques for stochastic convex and nonconvex optimization over networks. It is shown that the convergence rate of the proposed algorithm is


    for convex optimization, and


    for nonconvex optimization. The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives.


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    • A distributed stochastic Frank-Wolfe algorithm is proposed for stochastic optimization problems by judiciously combining Nesterov’s momentum and gradient tracking techniques
    • The convergence rate results of the proposed algorithm for convex and nonconvex problems are established, which, to the authors’ best knowledge, marks the first FW’s convergence rate results for distributed stochastic optimization
    • The efficacy of the algorithm is demonstrated by numerical simulations against a number of competing alternatives


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