One of the main advantages of second-order methods in a centralized setting is that they are insensitive to the condition number of the objective function's Hessian. For applications such as regression analysis, this means that less pre-processing of the data is required for the algorithm to work well, as the ill-conditioning caused by highly correlated variables will not be as problematic. Similar condition number independence has not yet been established for distributed methods. In this paper, we analyze the performance of a simple distributed second-order algorithm on quadratic problems and show that its convergence depends only logarithmically on the condition number. Our empirical results indicate that the use of second-order information can yield large efficiency improvements over first-order methods, both in terms of iterations and communications, when the condition number is of the same order of magnitude as the problem dimension.

中文翻译：

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图上的分布式牛顿法：二阶信息共享能否消除条件数依赖？

二阶方法在集中设置中的主要优点之一是它们对目标函数的 Hessian 的条件数不敏感。对于回归分析等应用，这意味着算法需要较少的数据预处理才能正常工作，因为由高度相关的变量引起的病态不会有问题。分布式方法尚未建立类似的条件数独立性。在本文中，我们分析了一个简单的分布式二阶算法在二次问题上的性能，并表明它的收敛仅在对数上取决于条件数。我们的实证结果表明，使用二阶信息可以比一阶方法产生更大的效率提升，