Analyzing random permutations for cyclic coordinate descent
Analyzing random permutations for cyclic coordinate descent
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DOI：
10.1090/mcom/3530
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发表时间：
2017-06
期刊：
影响因子：
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通讯作者：
Stephen J. Wright;Ching-pei Lee
中科院分区：
文献类型：
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作者：
Stephen J. Wright;Ching-pei Lee
我们考虑凸二次问题的坐标下降法，在每次迭代中进行精确的线搜索。(This算法与Gauss-Seidel在等价对称正定线性系统上的算法相同。我们描述了一类凸二次问题的随机置换版本的循环坐标下降（RPCD）优于标准的循环坐标下降（CCD）的方法，产生类似于完全随机变量（RCD）的收敛行为。收敛性分析的发展来解释的经验观察。
We consider coordinate descent methods on convex quadratic problems, in which exact line searches are performed at each iteration. (This algorithm is identical to Gauss-Seidel on the equivalent symmetric positive definite linear system.) We describe a class of convex quadratic problems for which the random-permutations version of cyclic coordinate descent (RPCD) outperforms the standard cyclic coordinate descent (CCD) approach, yielding convergence behavior similar to the fully-random variant (RCD). A convergence analysis is developed to explain the empirical observations.