University of Economics, Prague
In this paper, the authors develop and analyze Hydra: HYbriD cooRdinAte descent method for solving loss minimization problems with big data. They 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 computers and applies updates to the selected coordinates based on a simple closed-form formula. They 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.