关于随机聚集梯度法的收敛性

Figen OZTOPRAK TOPKAYA
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引用次数: 0

摘要

大量凸函数集合和的最小化问题在各种应用中都有出现。增量梯度、随机梯度和聚合梯度等方法是解决这些问题的常用方法,因为它们不需要在每次迭代中都进行完整的梯度评估。本文通过一种基于迭代线性系统收敛性的替代技术,对随机聚集梯度法进行了推广。该技术提供了二次情形下$O(\kappa^{-1})$线性收敛率的一个简短证明。我们观察到,对于一般情况,该技术是相当有限的,并且可以提供较弱的结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Convergence of Stochastic Aggregated Gradient Method
The minimization problem of the sum of a large set of convex functions arises in various applications. Methods such as incremental gradient, stochastic gradient, and aggregated gradient are popular choices for solving those problems as they do not require a full gradient evaluation at every iteration. In this paper, we analyze a generalization of the stochastic aggregated gradient method via an alternative technique based on the convergence of iterative linear systems. The technique provides a short proof for the $O(\kappa^{-1})$ linear convergence rate in the quadratic case. We observe that the technique is rather restrictive for the general case, and can provide weaker results.
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