Distributed Coordinate Descent Method for Learning with Big Data
This addresses the challenge of scaling machine learning to massive datasets for researchers and practitioners, though it is incremental as it builds on existing coordinate descent methods.
The paper tackles the problem of solving loss minimization with big data by developing Hydra, a hybrid coordinate descent method that partitions features across a cluster and updates random subsets in parallel, achieving bounds on iterations needed for high-probability approximate solutions and testing on a 3TB LASSO matrix.
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.