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Parallel Coordinate Descent Methods for Big Data Optimization

Peter Richtarik (peter.richtarik***at***ed.ac.uk)
Martin Takac (martin.taki***at***gmail.com)

Abstract: In this work we show that randomized (block) coordinate descent methods can be accelerated by parallelization when applied to the problem of minimizing the sum of a partially separable smooth convex function and a simple separable convex function. The theoretical speedup, as compared to the serial method, and referring to the number of iterations needed to approximately solve the problem with high probability, is a simple expression depending on the number of parallel processors and a natural and easily computable measure of separability of the smooth component of the objective function. In the worst case, when no degree of separability is present, there may be no speedup; in the best case, when the problem is separable, the speedup is equal to the number of processors. Our analysis also works in the mode when the number of blocks being updated at each iteration is random, which allows for modeling situations with busy or unreliable processors. We show that our algorithm is able to solve a LASSO problem involving a matrix with 20 billion nonzeros in 2 hours on a large memory node with 24 cores.

Keywords: Parallel coordinate descent, big data optimization, partial separability, huge-scale optimization, iteration complexity, expected separable over-approximation, composite objective, convex optimization, LASSO

Category 1: Convex and Nonsmooth Optimization (Convex Optimization )

Category 2: Optimization Software and Modeling Systems (Parallel Algorithms )

Citation: University of Edinburgh, November 2012

Download: [PDF]

Entry Submitted: 11/24/2012
Entry Accepted: 11/24/2012
Entry Last Modified: 12/04/2012

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