Learning distributed channel access policies for networked estimation: data-driven optimization in the mean-field regime

The problem of communicating sensor measurements over shared networks is prevalent in many modern large-scale distributed systems such as cyber-physical systems, wireless sensor networks and the internet of things. Due to bandwidth constraints, the system designer must jointly optimize decentralized medium access transmission and estimation policies that accommodate a very large number of devices in extremely contested environments such that the collection of all observations is reproduced at the destination with the best possible fidelity. We formulate a remote estimation problem in the mean-field regime where a very large number of sensors communicate their observations to an access point, or base-station, under a strict constraint on the maximum fraction of transmitting devices. We show that in the mean-field regime, this problem exhibits a structure which enables tractable optimization algorithms. More importantly, we obtain a data-driven learning scheme and a characterization of its convergence rate.