Systematic Design of Decentralized Algorithms for Consensus Optimization
Shuo Han

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.
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Taxonomy
TopicsDistributed Control Multi-Agent Systems · Neural Networks Stability and Synchronization · Advanced Memory and Neural Computing
