Testing fine-grained parallelism for the ADMM on a factor-graph

TL;DR

This paper introduces a problem-independent, message-passing based scheme to accelerate the ADMM algorithm for large-scale problems, achieving significant speedups on GPUs and multi-core CPUs without requiring parallel programming.

Contribution

It presents a novel, general approach to parallelize ADMM automatically via factor-graph interpretation, applicable across diverse domains without user-implemented parallel code.

Findings

Achieves 10-18x speedup on GPU

Achieves 5-9x speedup on multi-core CPUs

Applicable to combinatorial optimization, machine learning, and control

Abstract

There is an ongoing effort to develop tools that apply distributed computational resources to tackle large problems or reduce the time to solve them. In this context, the Alternating Direction Method of Multipliers (ADMM) arises as a method that can exploit distributed resources like the dual ascent method and has the robustness and improved convergence of the augmented Lagrangian method. Traditional approaches to accelerate the ADMM using multiple cores are problem-specific and often require multi-core programming. By contrast, we propose a problem-independent scheme of accelerating the ADMM that does not require the user to write any parallel code. We show that this scheme, an interpretation of the ADMM as a message-passing algorithm on a factor-graph, can automatically exploit fine-grained parallelism both in GPUs and shared-memory multi-core computers and achieves significant speedup in such diverse application domains as combinatorial optimization, machine learning, and optimal control. Specifically, we obtain 10-18x speedup using a GPU, and 5-9x using multiple CPU cores, over a serial, optimized C-version of the ADMM, which is similar to the typical speedup reported for existing GPU-accelerated libraries, including cuFFT (19x), cuBLAS (17x), and cuRAND (8x).