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Analyzing Random Permutations for Cyclic Coordinate Descent

Stephen J. Wright (swright***at***cs.wisc.edu)
Ching-pei Lee (ching-pei***at***cs.wisc.edu)

Abstract: 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.

Keywords: Coordinate descent, Gauss-Seidel, randomization, permutations

Category 1: Nonlinear Optimization (Unconstrained Optimization )

Citation: Technical Report, May, 2017

Download: [PDF]

Entry Submitted: 06/01/2017
Entry Accepted: 06/01/2017
Entry Last Modified: 02/19/2019

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