HBNET-GIANT: A communication-efficient accelerated Newton-type fully distributed optimization algorithm

TL;DR

HBNET-GIANT is a distributed second-order optimization algorithm that uses heavy-ball momentum to accelerate convergence for convex problems, outperforming existing methods in speed and efficiency.

Contribution

This work introduces HBNET-GIANT, a novel fully distributed Newton-type algorithm with momentum, providing rigorous convergence analysis and demonstrating significant acceleration over non-accelerated algorithms.

Findings

HBNET-GIANT achieves faster convergence than NETWORK-GIANT.

Heavy-ball momentum significantly accelerates the distributed optimization process.

Numerical experiments confirm the superior performance of HBNET-GIANT.

Abstract

This article presents a second-order fully distributed optimization algorithm, HBNET-GIANT, driven by heavy-ball momentum, for $L$-smooth and $\mu$-strongly convex objective functions. A rigorous convergence analysis is performed, and we demonstrate global linear convergence under certain sufficient conditions. Through extensive numerical experiments, we show that HBNET-GIANT with heavy-ball momentum achieves acceleration, and the corresponding rate of convergence is strictly faster than its non-accelerated version, NETWORK-GIANT. Moreover, we compare HBNET-GIANT with several state-of-the-art algorithms, both momentum-based and without momentum, and report significant performance improvement in convergence to the optimum. We believe that this work lays the groundwork for a broader class of second-order Newton-type algorithms with momentum and motivates further investigation into open problems, including an analytical proof of local acceleration in the fully distributed setting for convex optimization problems.