Decentralized Approximate Newton Methods for Convex Optimization on Networked Systems
Abstract
In this paper, a class of Decentralized Approximate Newton (DEAN) methods for addressing convex optimization on a networked system are developed, where nodes in the networked system seek for a consensus that minimizes the sum of their individual objective functions through local interactions only. The proposed DEAN algorithms allow each node to repeatedly perform a local approximate Newton update, which leverages tracking the global Newton direction and dissipating the discrepancies among the nodes. Under less restrictive problem assumptions in comparison with most existing second-order methods, the DEAN algorithms enable the nodes to reach a consensus that can be arbitrarily close to the optimum. Moreover, for a particular DEAN algorithm, the nodes linearly converge to a common suboptimal solution with an explicit error bound. Finally, simulations demonstrate the competitive performance of DEAN in convergence speed, accuracy, and efficiency.
Cite
@article{arxiv.1903.09481,
title = {Decentralized Approximate Newton Methods for Convex Optimization on Networked Systems},
author = {Hejie Wei and Zhihai Qu and Xuyang Wu and Hao Wang and Jie Lu},
journal= {arXiv preprint arXiv:1903.09481},
year = {2020}
}