  We propose a communication and computation efficient second-order method for
distributed 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 the
similar 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 problem
by $\mathcal{O}\big(\sqrt{dL}\,\epsilon^{-3/2}\big)$ iterations, where $L$ is
the Lipschitz constant of Hessian. Moreover, it enjoys a local superlinear
convergence under the strongly-convex assumption. Experiments on both convex
and nonconvex problems show that our proposed method performs significantly
better than baselines.
