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Distributed Coordinate Descent Method for Learning with Big Data

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arxiv 1310.2059 v1 pith:35DXAC3Z submitted 2013-10-08 stat.ML cs.DCcs.LGmath.OC

Distributed Coordinate Descent Method for Learning with Big Data

classification stat.ML cs.DCcs.LGmath.OC
keywords coordinatesdatacoordinatedescentmethodnodepartitionanalyze
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved
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In this paper we develop and analyze Hydra: HYbriD cooRdinAte descent method for solving loss minimization problems with big data. We initially partition the coordinates (features) and assign each partition to a different node of a cluster. At every iteration, each node picks a random subset of the coordinates from those it owns, independently from the other computers, and in parallel computes and applies updates to the selected coordinates based on a simple closed-form formula. We give bounds on the number of iterations sufficient to approximately solve the problem with high probability, and show how it depends on the data and on the partitioning. We perform numerical experiments with a LASSO instance described by a 3TB matrix.

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