Performance evaluation and analysis of distributed multi-agent optimization algorithms with sparsified directed communication

Abstract

There has been significant interest in distributed optimization algorithms, motivated by applications in Big Data analytics, smart grid, vehicle networks, etc. While there have been extensive theory and theoretical advances, a proportionally small body of scientific literature focuses on numerical evaluation of the proposed methods in actual practical, parallel programming environments. This paper considers a general algorithmic framework of first and second order methods with sparsified communications and computations across worker nodes. The considered framework subsumes several existing methods. In addition, a novel method that utilizes unidirectional sparsified communications is introduced and theoretical convergence analysis is also provided. Namely, we prove R-linear convergence in the expected norm. A thorough empirical evaluation of the methods using Message Passing Interface (MPI) on a High Performance Computing (HPC) cluster is carried out and several useful insights and guidelines on the performance of algorithms and inherent communication-computational trade-offs in a realistic setting are derived.