Distributed Coordinate Descent Method for Learning with Big Data

TL;DR

This paper introduces Hydra, a distributed coordinate descent algorithm designed for large-scale data, which partitions features across nodes and updates randomly selected coordinates in parallel, with theoretical bounds and practical experiments.

Contribution

Hydra is a novel distributed coordinate descent method that efficiently handles big data by parallelizing coordinate updates across cluster nodes with theoretical convergence guarantees.

Findings

Achieves efficient optimization on 3TB LASSO data

Provides bounds on iteration complexity based on data and partitioning

Demonstrates practical scalability and effectiveness

Abstract

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.