# Distributed Block Coordinate Descent for Minimizing Partially Separable Functions

arXiv: https://arxiv.org/abs/1406.0238 · HTML: https://mlsanity.com/paper/1406.0238/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Jun 2014.

## Built on by (most cited first, 3 of 3)

- [Multilevel Objective-Function-Free Optimization with an Application to Neural Networks Training](https://mlsanity.com/paper/2302.07049/) (2023)
- [Distributed stochastic optimization with large delays](https://mlsanity.com/paper/2107.02919/) (2021)
- [FLECS-CGD: A Federated Learning Second-Order Framework via Compression and Sketching with Compressed Gradient Differences](https://mlsanity.com/paper/2210.09626/) (2022)

## Abstract (arXiv)

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.