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In this paper we develop and analyze Hydra: HYbriD cooRdinAte descent methodfor solving loss minimization problems with big data. We initially partitionthe coordinates (features) and assign each partition to a different node of acluster. At every iteration, each node picks a random subset of the coordinatesfrom those it owns, independently from the other computers, and in parallelcomputes and applies updates to the selected coordinates based on a simpleclosed-form formula. We give bounds on the number of iterations sufficient toapproximately solve the problem with high probability, and show how it dependson the data and on the partitioning. We perform numerical experiments with aLASSO instance described by a 3TB matrix.

Distributed Coordinate Descent Method for Learning with Big Data