Stability and Convergence of Distributed Stochastic Approximations with large Unbounded Stochastic Information Delays. (arXiv:2305.07091v1 [math.OC])

We generalize the Borkar-Meyn stability Theorem (BMT) to distributed
stochastic approximations (SAs) with information delays that possess an
arbitrary moment bound. To model the delays, we introduce Age of Information
Processes (AoIPs): stochastic processes on the non-negative integers with a
unit growth property. We show that AoIPs with an arbitrary moment bound cannot
exceed any fraction of time infinitely often. In combination with a suitably
chosen stepsize, this property turns out to be sufficient for the stability of
distributed SAs. …

age arxiv convergence distributed growth information math negative processes property sas show stochastic theorem