Distributed Block Coordinate Descent for Minimizing Partially Separable Functions

TL;DR

This paper introduces a distributed randomized block coordinate descent method for large-scale convex optimization, analyzing how partial separability affects complexity and demonstrating its effectiveness in distributed computing environments.

Contribution

It extends existing coordinate descent methods to distributed settings for partially separable functions, providing complexity analysis and practical implementation strategies.

Findings

Complexity depends on the degree of separability.

The method is effective in distributed multi-core environments.

Promising computational results demonstrate practical viability.

Abstract

In this work we propose a distributed randomized block coordinate descent method for minimizing a convex function with a huge number of variables/coordinates. We analyze its complexity under the assumption that the smooth part of the objective function is partially block separable, and show that the degree of separability directly influences the complexity. This extends the results in [Richtarik, Takac: Parallel coordinate descent methods for big data optimization] to a distributed environment. We first show that partially block separable functions admit an expected separable overapproximation (ESO) with respect to a distributed sampling, compute the ESO parameters, and then specialize complexity results from recent literature that hold under the generic ESO assumption. We describe several approaches to distribution and synchronization of the computation across a cluster of multi-core computers and provide promising computational results.