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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2507.16601 |
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| _version_ | 1866912496829333504 |
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| author | Gerencsér, Balázs Kornyik, Miklós |
| author_facet | Gerencsér, Balázs Kornyik, Miklós |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16601 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Low complexity convergence rate bounds for push-sum algorithms with homogeneous correlation structure Gerencsér, Balázs Kornyik, Miklós Probability Multiagent Systems 37M25 (Primary) 93D50, 93D05 (Secondary} G.3 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. |
| title | Low complexity convergence rate bounds for push-sum algorithms with homogeneous correlation structure |
| topic | Probability Multiagent Systems 37M25 (Primary) 93D50, 93D05 (Secondary} G.3 |
| url | https://arxiv.org/abs/2507.16601 |