论文标题
一类精确的一阶分布方法的线性收敛率分析，用于重量均衡的时间变化网络和不协调的步骤尺寸
Linear Convergence Rate Analysis of a Class of Exact First-Order Distributed Methods for Weight-Balanced Time-Varying Networks and Uncoordinated Step Sizes
论文作者
论文摘要
我们在基础网络和台阶上的一般设置下分析了一类精确分布的一阶方法。更详细地，我们允许同时进行随时间变化的不协调的步骤和时变的定向重量平衡网络，并在有限的间隔内共同连接。分析的方法类别涵盖了几种现有的算法，例如统一的额外和统一挖掘（Jakovetic，2019年）或确切的光谱梯度方法（Jakovetic，Krejic，Krejic，Krklec Jerinkic，2019年，2019年），这些方法已在更多的限制性假设下进行了分析。在假定的环境下，我们建立了方法的R线性收敛，并提出了我们的结果对文献的几种含义。最值得注意的是，我们表明（Jakovetic，2019年）中的统一策略和（Jakovetic，Krejic，Krejic，Krklec Jerinkic，2019年）中的光谱尺寸选择策略具有高度的鲁棒性，可对无协调的时间变化级别尺寸和时间变化的网络表现出高度的稳健性。
We analyze a class of exact distributed first order methods under a general setting on the underlying network and step-sizes. In more detail, we allow simultaneously for time-varying uncoordinated stepsizes and time-varying directed weight-balanced networks, jointly connected over bounded intervals. The analyzed class of methods subsumes several existing algorithms like the unified Extra and unified DIGing (Jakovetic, 2019), or the exact spectral gradient method (Jakovetic, Krejic, Krklec Jerinkic, 2019) that have been analyzed before under more restrictive assumptions. Under the assumed setting, we establish R-linear convergence of the methods and present several implications that our results have on the literature. Most notably, we show that the unification strategy in (Jakovetic, 2019) and the spectral step-size selection strategy in (Jakovetic, Krejic, Krklec Jerinkic, 2019) exhibit a high degree of robustness to uncoordinated time-varying step sizes and to time-varying networks.
