论文标题
牛顿跟踪算法具有精确的线性收敛速率，用于分散共识优化
A Newton Tracking Algorithm with Exact Linear Convergence Rate for Decentralized Consensus Optimization
论文作者
论文摘要
本文考虑了通过网络定义的分散的共识优化问题，每个节点都具有二阶可区分的本地目标函数。我们的目标是最大程度地减少局部目标函数的总结，并仅使用本地计算和相邻通信找到确切的最佳解决方案。我们提出了一种新颖的牛顿跟踪算法，每个节点都沿着纽顿的本地牛顿方向更新其本地变量，并通过相邻和历史信息修改。我们研究了拟议的牛顿跟踪算法与几种现有方法（包括梯度跟踪和二阶算法）之间的连接。在强大的凸度假设下，我们证明它以线性速率收敛到确切的最佳解决方案。数值实验证明了牛顿跟踪的功效并验证了理论发现。
This paper considers the decentralized consensus optimization problem defined over a network where each node holds a second-order differentiable local objective function. Our goal is to minimize the summation of local objective functions and find the exact optimal solution using only local computation and neighboring communication. We propose a novel Newton tracking algorithm, where each node updates its local variable along a local Newton direction modified with neighboring and historical information. We investigate the connections between the proposed Newton tracking algorithm and several existing methods, including gradient tracking and second-order algorithms. Under the strong convexity assumption, we prove that it converges to the exact optimal solution at a linear rate. Numerical experiments demonstrate the efficacy of Newton tracking and validate the theoretical findings.
