  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.
