  We propose a distributed, cubic-regularized Newton method for large-scale
convex optimization over networks. The proposed method requires only local
computations and communications and is suitable for federated learning
applications over arbitrary network topologies. We show a $O(k^{{-}3})$
convergence rate when the cost function is convex with Lipschitz gradient and
Hessian, with $k$ being the number of iterations. We further provide
network-dependent bounds for the communication required in each step of the
algorithm. We provide numerical experiments that validate our theoretical
results.
