Communication Lower Bounds for Distributed Convex Optimization: Partition Data on Features
This work addresses communication efficiency challenges for researchers and practitioners in distributed optimization, particularly when dealing with high-dimensional data, but it is incremental as it builds on existing lower bound analyses.
The paper tackles the problem of understanding inherent limitations in distributed convex optimization when data is partitioned on features, developing tight lower bounds on communication rounds for non-incremental algorithms and a lower bound for incremental algorithms under certain communication restrictions.
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.