Communication Lower Bounds for Distributed Convex Optimization: Partition Data on Features

TL;DR

This paper establishes fundamental lower bounds on communication rounds for distributed convex optimization algorithms when data is partitioned on features, highlighting inherent limitations in such settings.

Contribution

It develops tight lower bounds for non-incremental and incremental algorithms in feature-partitioned distributed convex optimization.

Findings

Tight lower bounds on communication rounds for non-incremental algorithms.

Lower bounds for randomized incremental algorithms.

Insights into the limitations of distributed convex optimization with feature partitioning.

Abstract

Recently, there has been an increasing interest in designing distributed convex optimization algorithms under the setting where the data matrix is partitioned on features. Algorithms under this setting sometimes have many advantages over those under the setting where data is partitioned on samples, especially when the number of features is huge. Therefore, it is important to understand the inherent limitations of these optimization problems. In this paper, with certain restrictions on the communication allowed in the procedures, we develop tight lower bounds on communication rounds for a broad class of non-incremental algorithms under this setting. We also provide a lower bound on communication rounds for a class of (randomized) incremental algorithms.