Low complexity convergence rate bounds for push-sum algorithms with homogeneous correlation structure
The objective of this work is to establish an upper bound for the almost sure convergence rate for a class of push-sum algorithms. The current work extends the methods and results of the authors on a similar low-complexity bound on push-sum algorithms with some particular synchronous message passing...
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| Main Authors | , |
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| Format | Journal Article |
| Language | English |
| Published |
22.07.2025
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| Subjects | |
| Online Access | Get full text |
| DOI | 10.48550/arxiv.2507.16601 |
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| Summary: | The objective of this work is to establish an upper bound for the almost sure convergence rate for a class of push-sum algorithms. The current work extends the methods and results of the authors on a similar low-complexity bound on push-sum algorithms with some particular synchronous message passing schemes and complements the general approach of Gerencsér and Gerencsér from 2022 providing an exact, but often less accessible description. Furthermore, a parametric analysis is presented on the ``weight'' of the messages, which is found to be convex with an explicit expression for the gradient. This allows the fine-tuning of the algorithm used for improved efficiency. Numerical results confirm the speedup in evaluating the computable bounds without deteriorating their performance, for a graph on 120 vertices the runtime drops by more than 4 orders of magnitude. |
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| DOI: | 10.48550/arxiv.2507.16601 |