Network-GIANT: Fully distributed Newton-type optimization via harmonic Hessian consensus
Abstract
This paper considers the problem of distributed multi-agent learning, where the global aim is to minimize a sum of local objective (empirical loss) functions through local optimization and information exchange between neighbouring nodes. We introduce a Newton-type fully distributed optimization algorithm, Network-GIANT, which is based on GIANT, a Federated learning algorithm that relies on a centralized parameter server. The Network-GIANT algorithm is designed via a combination of gradient-tracking and a Newton-type iterative algorithm at each node with consensus based averaging of local gradient and Newton updates. We prove that our algorithm guarantees semi-global and exponential convergence to the exact solution over the network assuming strongly convex and smooth loss functions. We provide empirical evidence of the superior convergence performance of Network-GIANT over other state-of-art distributed learning algorithms such as Network-DANE and Newton-Raphson Consensus.
Cite
@article{arxiv.2305.07898,
title = {Network-GIANT: Fully distributed Newton-type optimization via harmonic Hessian consensus},
author = {Alessio Maritan and Ganesh Sharma and Luca Schenato and Subhrakanti Dey},
journal= {arXiv preprint arXiv:2305.07898},
year = {2023}
}