论文标题
一种分布式的立方规范化的牛顿方法，用于在网络上平滑凸优化
A Distributed Cubic-Regularized Newton Method for Smooth Convex Optimization over Networks
论文作者
论文摘要
我们提出了一种分布式的，立方体调节的牛顿方法，用于网络上的大规模凸优化。所提出的方法仅需要本地计算和通信，并且适用于任意网络拓扑的联合学习应用程序。当成本函数带有Lipschitz渐变和Hessian时，我们显示$ O（k^{{ - } 3}）$收敛率，$ k $是迭代的数量。我们进一步为算法的每个步骤中所需的通信提供了依赖网络的界限。我们提供数值实验来验证我们的理论结果。
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.
