Distributed inexact Newton method with adaptive step sizes
提出DINAS方法，用于分布式网络中的个性化优化和共识优化，采用自适应大步长，无需局部Hessian逆计算或通信，在个性化学习中实现计算二次收敛和通信线性收敛，数值实验优于现有方法。
nodes in a generic connected network solve a problem of common interest: distributed personalized optimization and consensus optimization. A new method termed DINAS (Distributed Inexact Newton method with Adaptive step size) is proposed. DINAS employs large adaptively computed step sizes, requires a reduced global parameters knowledge with respect to existing alternatives, and can operate without any local Hessian inverse calculations nor Hessian communications. When solving personalized distributed learning formulations, DINAS achieves quadratic convergence with respect to computational cost and linear convergence with respect to communication cost, the latter rate being independent of the local functions condition numbers or of the network topology. When solving consensus optimization problems, DINAS is shown to converge to the global solution. Extensive numerical experiments demonstrate significant improvements of DINAS over existing alternatives. As a result of independent interest, we provide for the first time convergence analysis of the Newton method with the adaptive Polyak's step size when the Newton direction is computed inexactly in centralized environment.