Systematic Design of Decentralized Algorithms for Consensus Optimization

TL;DR

This paper introduces a systematic, modular approach for designing decentralized algorithms for consensus optimization by combining base algorithms with consensus tracking, supported by an IQC-based convergence analysis.

Contribution

It presents a separation principle that simplifies the design and analysis of decentralized algorithms using a modular framework and IQCs, demonstrated with ADMM-based algorithms.

Findings

Modular separation principle for decentralized algorithms

IQC-based automated convergence analysis framework

Design and analysis of ADMM-based decentralized algorithm

Abstract

We propose a separation principle that enables a systematic way of designing decentralized algorithms used in consensus optimization. Specifically, we show that a decentralized optimization algorithm can be constructed by combining a non-decentralized base optimization algorithm and decentralized consensus tracking. The separation principle provides modularity in both the design and analysis of algorithms under an automated convergence analysis framework using integral quadratic constraints (IQCs). We show that consensus tracking can be incorporated into the IQC-based analysis. The workflow is illustrated through the design and analysis of a decentralized algorithm based on the alternating direction method of multipliers.