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We propose a communication and computation efficient second-order method fordistributed optimization. For each iteration, our method only requires$\mathcal{O}(d)$ communication complexity, where $d$ is the problem dimension.We also provide theoretical analysis to show the proposed method has thesimilar convergence rate as the classical second-order optimization algorithms.Concretely, our method can find~$\big(\epsilon,\sqrt{dL\epsilon}\,\big)$-second-order stationary points for nonconvex problemby $\mathcal{O}\big(\sqrt{dL}\,\epsilon^{-3/2}\big)$ iterations, where $L$ isthe Lipschitz constant of Hessian. Moreover, it enjoys a local superlinearconvergence under the strongly-convex assumption. Experiments on both convexand nonconvex problems show that our proposed method performs significantlybetter than baselines.

Communication Efficient Distributed Newton Method with Fast Convergence Rates