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arXiv · 2007.03562

A Distributed Cubic-Regularized Newton Method for Smooth Convex Optimization over Networks

César A. Uribe·Ali Jadbabaie
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Abstract

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.

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BibTeXRIS

César A. Uribe, Ali Jadbabaie. 2020-07-07. A Distributed Cubic-Regularized Newton Method for Smooth Convex Optimization over Networks. https://arxiv.org/abs/2007.03562

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