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.
@article{arxiv.2511.06379,
title = {A Poisson Jump-driven SDE Approach to Distributed Gradient Descent with Sparse Communication},
author = {Marc Weber and John Paul Strachan and Christian Ebenbauer},
journal= {arXiv preprint arXiv:2511.06379},
year = {2025}
}