This white paper introduces aoip.ai, a groundbreaking open-source SDK incorporating peer-to-peer technology and advanced AI integration to transform VoIP and IoT applications. It addresses key market challenges by enhancing data security, elevating communication quality, and providing greater flexibility for developers and users. Developed in collaboration with Carnegie Mellon University, aoip.ai sets a new standard for decentralized and democratized communication solutions.

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. Compared to the BMT, our analysis requires crucial modifications and a new line of argument to handle the SA errors caused by AoI. In our analysis, we show that these SA errors satisfy a recursive inequality. To evaluate this recursion, we propose a new Gronwall-type inequality for time-varying lower limits of summations. As applications to our distributed BMT, we discuss distributed gradient-based optimization and a new approach to analyzing SAs with momentum.