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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.

# 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)
• 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

\begin{document}${\cal{O}}(k^{-\frac{1}{2}})$\end{document}

for convex optimization, and

${\cal{O}}(1/\mathrm{log}_2(k))$

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

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