{"ID":2844368,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2511.06379","arxiv_id":"2511.06379","title":"A Poisson Jump-driven SDE Approach to Distributed Gradient Descent with Sparse Communication","abstract":"To bridge the gap between idealised communication models and the stochastic reality of networked systems, we introduce a framework for embedding asynchronous communication directly into algorithm dynamics using stochastic differential equations (SDE) driven by Poisson Jumps. We apply this communication-aware design to the continuous-time gradient flow, yielding a distributed algorithm where updates occur via sparse Poisson events. Our analysis establishes communication rate bounds for asymptotic stability and, crucially, a higher, yet sparse, rate that provably any desired exponential convergence performance slower than the nominal, centralized flow. These theoretical results, shown for unconstrained quadratic optimisation, are validated by a numerical simulation.","short_abstract":"To bridge the gap between idealised communication models and the stochastic reality of networked systems, we introduce a framework for embedding asynchronous communication directly into algorithm dynamics using stochastic differential equations (SDE) driven by Poisson Jumps. We apply this communication-aware design to...","url_abs":"https://arxiv.org/abs/2511.06379","url_pdf":"https://arxiv.org/pdf/2511.06379v1","authors":"[\"Marc Weber\",\"John Paul Strachan\",\"Christian Ebenbauer\"]","published":"2025-11-09T13:32:39Z","proceeding":"math.OC","tasks":"[\"math.OC\"]","methods":"[]","has_code":false}