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arXiv · 1806.08537

Subgradient-Free Stochastic Optimization Algorithm for Non-smooth Convex Functions over Time-Varying Networks

Yinghui Wang·Wenxiao Zhao·Yiguang Hong·Mohsen Zamani
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Abstract

In this paper we consider a distributed stochastic optimization problem without the gradient/subgradient information for the local objective functions, subject to local convex constraints. The objective functions may be non-smooth and observed with stochastic noises, and the network for the distributed design is time-varying. By adding the stochastic dithers into the local objective functions and constructing the randomized differences motivated by the Kiefer-Wolfowitz algorithm, we propose a distributed subgradient-free algorithm to find the global minimizer with local observations. Moreover, we prove that the consensus of estimates and global minimization can be achieved with probability one over the time-varying network, and then obtain the convergence rate of the mean average of estimates as well. Finally, we give a numerical example to illustrate the effectiveness of the proposed algorithm.

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Yinghui Wang, Wenxiao Zhao, Yiguang Hong, Mohsen Zamani. 2018-06-22. Subgradient-Free Stochastic Optimization Algorithm for Non-smooth Convex Functions over Time-Varying Networks. https://arxiv.org/abs/1806.08537

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