A General Analysis of the Convergence of ADMM

Authors: Robert Nishihara, Laurent Lessard, Ben Recht, Andrew Packard, Michael Jordan

ICML 2015 | Conference PDF | Archive PDF | Plain Text | LLM Run Details

Reproducibility Variable Result LLM Response
Research Type Experimental On a numerical example, we demonstrate that minimizing the derived bound on the convergence rate provides a practical approach to selecting algorithm parameters for particular ADMM instances. We complement our upper bound by constructing a nearly-matching lower bound on the worst-case rate of convergence.
Researcher Affiliation Academia Robert Nishihara RKN@EECS.BERKELEY.EDU Laurent Lessard LESSARD@BERKELEY.EDU Benjamin Recht BRECHT@EECS.BERKELEY.EDU Andrew Packard APACKARD@BERKELEY.EDU Michael I. Jordan JORDAN@EECS.BERKELEY.EDU University of California, Berkeley, CA 94720 USA
Pseudocode Yes Algorithm 1 Alternating Direction Method of Multipliers; Algorithm 2 Over-Relaxed Alternating Direction Method of Multipliers
Open Source Code No No explicit statement or link providing access to the source code for the methodology described in the paper was found.
Open Datasets No The paper uses a synthetically generated dataset for a distributed Lasso problem: 'Each Ai is generated by populating a 600 500 matrix with independent standard normal entries and normalizing the columns. We generate each bi via bi = Aix0 + εi, where x0 is a sparse 500-dimensional vector with 250 independent standard normal entries, and εi N(0, 10 3I).' This is not a publicly available dataset with concrete access information.
Dataset Splits No The paper describes numerical examples on a synthetically generated dataset to demonstrate convergence, but it does not specify any training, validation, or test dataset splits.
Hardware Specification No No specific hardware details (e.g., GPU/CPU models, memory specifications) used for running the experiments are mentioned in the paper.
Software Dependencies No The paper does not list specific software dependencies with version numbers (e.g., programming languages, libraries, or solvers with their exact versions) used for the implementation or experiments.
Experiment Setup Yes For the distributed Lasso problem, the paper specifies experimental parameters and data generation details: 'we choose N = 5 and µ = 0.1. Each Ai is generated by populating a 600 500 matrix with independent standard normal entries and normalizing the columns. We generate each bi via bi = Aix0 + εi, where x0 is a sparse 500-dimensional vector with 250 independent standard normal entries, and εi N(0, 10 3I).'