Subgradient-Free Stochastic Optimization Algorithm for Non-smooth Convex Functions over Time-Varying Networks
Year: 2018
Type: preprint
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.
Source: arXiv (Cornell University)
Language: English
Subfield: Computer Networks and Communications
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2810184945