{"ID":2891827,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2507.16601","arxiv_id":"2507.16601","title":"Low complexity convergence rate bounds for push-sum algorithms with homogeneous correlation structure","abstract":"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.","short_abstract":"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 complem...","url_abs":"https://arxiv.org/abs/2507.16601","url_pdf":"https://arxiv.org/pdf/2507.16601v1","authors":"[\"Balázs Gerencsér\",\"Miklós Kornyik\"]","published":"2025-07-22T13:58:06Z","proceeding":"math.PR","tasks":"[\"math.PR\",\"cs.MA\"]","methods":"[]","has_code":false}