A Poisson Jump-driven SDE Approach to Distributed Gradient Descent with Sparse Communication

arXiv (Cornell University)

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.

Authors 2

1. John Paul Strachan
2. Christian Ebenbauer Aachen

   RWTH Aachen University

   Affiliation as printed

   RWTH Aachen