Systematic Design of Decentralized Algorithms for Consensus Optimization
This work offers a modular design and analysis methodology for decentralized optimization, benefiting researchers and practitioners in distributed systems.
The paper proposes a separation principle for systematically designing decentralized consensus optimization algorithms by combining a non-decentralized base algorithm with decentralized consensus tracking, and provides an automated convergence analysis framework using integral quadratic constraints.
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.