Neural Approximation of Open-Loop Feedback Rate Control in Satellite Networks

Abstract

A resource allocation problem for a satellite network is considered, where variations of fading conditions are added to those of traffic load. Since the capacity of the system is finite and divided in finite discrete portions, the resource allocation problem reveals to be a discrete stochastic programming one, which is typically NP-Hard. In practice, a good approximation of the optimal solution could be obtained through the adoption of a closed-form expression of the performance measure in steady-state conditions. Once we have summarized the drawbacks of such optimization strategy, we address two novel optimization approaches. The first one derives from Gokbayrak and Cassandras and is based on the minimization over the discrete constraint set using an estimate of the gradient, obtained through a "relaxed continuous extension" of the performance measure. The computation of the gradient estimation is based on infinitesimal perturbation analysis (IPA). Neither closed forms of the performance measures, nor additional feedbacks concerning the state of the system and very mild assumptions about the stochastic environment are requested. The second one is the main contribution of the present work, and is based on an open-loop feedback control (OLFC) strategy, aimed at providing optimal reallocation strategies as functions of the state of the network. The optimization approach leads us to a functional optimization problem, and we investigate the adoption of a neural network-based technique, in order to approximate its solution. As is shown in the simulation results, we obtain near-optimal reallocation strategies with a small real time computational effort and avoid the suboptimal transient periods introduced by the IPA gradient descent algorithm.