Distributed consensus and optimization under communication delays
Abstract
We study the effects of communication delays in distributed consensus and optimization algorithms. We propose two ways to model delays. First, assuming each edge of a communication network has a fixed delay, we characterize the consensus value exactly as a function of the delays and edge weights and obtain convergence rate bounds using results from non-reversible Markov chains. Second, we propose a novel way to model random delays per edge. Our model allows the reception of multiple delayed messages from the same sender in the same time slot, a situation that can happen in practice. Both models admit a description of the consensus updates in the presence of delays via linear equations. Finally, we briefly discuss how to apply our delay models to analyze distributed optimization algorithms in the presence of delayed information.
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All prior work in distributed optimization, except for [30], [31], [32], [29], requires time-varying communications with some form of balancedness, often reflected in a requirement of having a sequence of doubly stochastic matrices commensurate with the sequence of underlying communication graphs.
“All the prior work in distributed optimization, except for [30], [31], [32], [29], requires time-varying communications with some form of balancedness, often reflected in a requirement of having a sequence of doubly stochastic matrices that are commensurate with the sequence of underlying communication graphs.”
From Distributed Optimization Over Time-Varying Directed Graphs (2015) · cites this paper as [32]
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References 21 · Cited by 92
- Authors
- Tsianos, K. I., & Rabbat, M. G.
- Affiliations
- McGill University (CA)
- ORCID
- Rabbat, Michael G.
- Venue
- 2011 49th Annual Allerton Conference on Communication, Control, and Computing (Allerton)
- Publisher
- IEEE
- Published
- 2011-09
- Pages
- 974-982
- OpenAlex
- W2169167445
- Cited by
- 92
- References
- 21
- Citations by year
- 2026: 1 · 2025: 5 · 2024: 5 · 2023: 7 · 2022: 1 · 2021: 10 · 2020: 10 · 2019: 5 · 2018: 11 · 2017: 4 · 2016: 10 · 2015: 6 · 2014: 4 · 2013: 4 · 2012: 7
- FWCI
- 4.84
- Type
- conference paper
- Language
- en
- Open access
- closed
- Locations
- Allerton Conference on Communication, Control, and Computing (publishedVersion)
- Topics
- Physical Sciences › Computer Science › Computer Networks and Communications › Distributed Control Multi-Agent Systems
- Physical Sciences › Engineering › Control and Systems Engineering › Stability and Control of Uncertain Systems
- Physical Sciences › Computer Science › Computer Networks and Communications › Neural Networks Stability and Synchronization
- Keywords
- distributed consensus, communication delay, distributed optimization, convergence rate bounds, non-reversible Markov chains, communication networks
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