A Distributed Cubic-Regularized Newton Method for Smooth Convex Optimization over Networks
This addresses efficient federated learning over arbitrary network topologies, though it appears incremental as it builds on existing cubic-regularized Newton methods.
The authors tackled distributed convex optimization over networks by proposing a cubic-regularized Newton method that requires only local computations and communications, achieving an O(k^{-3}) convergence rate for functions with Lipschitz gradient and Hessian.
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.