Network-GIANT: Fully distributed Newton-type optimization via harmonic Hessian consensus

• URL: http://arxiv.org/abs/2305.07898v2
• Date: Wed, 19 Jul 2023 09:15:20 GMT
• Title: Network-GIANT: Fully distributed Newton-type optimization via harmonic Hessian consensus
• Authors: Alessio Maritan, Ganesh Sharma, Luca Schenato, Subhrakanti Dey
• Abstract summary: We introduce a Newton-type fully distributed optimization algorithm, Network-GIANT, based on GIANT. 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.
• Score: 2.8617826964327113
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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.

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