  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.
