{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/communication-efficient-distributed-newton-1","title":"Communication Efficient Distributed Newton Method with Fast Convergence Rates","arxiv_id":"2305.17945","date":"2023-05-29","proceeding":null,"authors":["Chengchang Liu","Lesi Chen","Luo Luo","John C. S. Lui"],"abstract":"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. 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