Quantized Consensus ADMM for Multi-Agent Distributed Optimization

Abstract

Multi-agent distributed optimization over a network minimizes a global objective formed by a sum of local convex functions using only local computation and communication. We develop and analyze a quantized distributed algorithm based on the alternating direction method of multipliers (ADMM) when inter-agent communications are subject to finite capacity and other practical constraints. While existing quantized ADMM approaches only work for quadratic local objectives, the proposed algorithm can deal with more general objective functions (possibly non-smooth) including the LASSO. Under certain convexity assumptions, our algorithm converges to a consensus within ${\log }_{1+\eta }\Omega$ iterations, where $\eta >0$ depends on the local objectives and the network topology, and $\Omega$ is a polynomial determined by the quantization resolution, the distance between initial and optimal variable values, the local objective functions and the network topology. A tight upper bound on the consensus error is also obtained which does not depend on the size of the network.

30 pages, 4 figures; to be submitted to IEEE Trans. Signal Processing. arXiv admin note: text overlap with arXiv:1307.5561 by other authors

References in corpus (4)

• Multi-Agent Distributed Optimization via Inexact Consensus ADMM
• On the Linear Convergence of the Alternating Direction Method of Multipliers
• Quantized Consensus ADMM for Multi-Agent Distributed Optimization
• Quantized Consensus by the ADMM: Probabilistic versus Deterministic Quantizers

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• Distributed ADMM with Synergetic Communication and Computation
• COKE: Communication-Censored Decentralized Kernel Learning
• Optimized Quantization in Distributed Graph Signal Filtering
• New results on multi-agent system consensus: A graph signal processing perspective