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Recent Newton-type federated learning algorithms have demonstrated linearconvergence with respect to the communication rounds. However, communicatingHessian matrices is often unfeasible due to their quadratic communicationcomplexity. In this paper, we introduce a novel approach to tackle this issuewhile still achieving fast convergence rates. Our proposed method, named asFederated Newton Sketch methods (FedNS), approximates the centralized Newton'smethod by communicating the sketched square-root Hessian instead of the exactHessian. To enhance communication efficiency, we reduce the sketch size tomatch the effective dimension of the Hessian matrix. We provide convergenceanalysis based on statistical learning for the federated Newton sketchapproaches. Specifically, our approaches reach super-linear convergence ratesw.r.t. the communication rounds for the first time. We validate theeffectiveness of our algorithms through various experiments, which coincidewith our theoretical findings.

FedNS: A Fast Sketching Newton-Type Algorithm for Federated Learning