Analysis of Distributed ADMM Algorithm for Consensus Optimization in Presence of Error
Layla Majzoobi, Farshad Lahouti
TL;DR
This paper analyzes how distributed ADMM algorithms for consensus optimization behave when nodes introduce errors, showing linear convergence under certain conditions and providing numerical validation.
Contribution
It offers a novel convergence analysis of distributed ADMM in the presence of additive node errors, including conditions for linear convergence and insights into convergence points.
Findings
ADMM converges linearly despite node errors under specific conditions
The convergence point is characterized in the presence of additive noise
Numerical results confirm the theoretical analysis
Abstract
ADMM is a popular algorithm for solving convex optimization problems. Applying this algorithm to distributed consensus optimization problem results in a fully distributed iterative solution which relies on processing at the nodes and communication between neighbors. Local computations usually suffer from different types of errors, due to e.g., observation or quantization noise, which can degrade the performance of the algorithm. In this work, we focus on analyzing the convergence behavior of distributed ADMM for consensus optimization in presence of additive node error. We specifically show that (a noisy) ADMM converges linearly under certain conditions and also examine the associated convergence point. Numerical results are provided which demonstrate the effectiveness of the presented analysis.
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Taxonomy
TopicsDistributed Control Multi-Agent Systems · Stochastic Gradient Optimization Techniques · Energy Efficient Wireless Sensor Networks
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