Network-GIANT: Fully distributed Newton-type optimization via harmonic Hessian consensus
This addresses the problem of efficient distributed optimization for multi-agent systems, offering a fully decentralized approach that is incremental over existing federated learning methods.
The paper tackles distributed multi-agent learning by proposing Network-GIANT, a fully distributed Newton-type optimization algorithm that eliminates the need for a centralized server, and demonstrates semi-global exponential convergence to the exact solution with superior empirical performance over state-of-the-art methods like Network-DANE and Newton-Raphson Consensus.
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.