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The problem of communicating sensor measurements over shared networks isprevalent in many modern large-scale distributed systems such as cyber-physicalsystems, wireless sensor networks, and the internet of things. Due to bandwidthconstraints, the system designer must jointly design decentralized mediumaccess transmission and estimation policies that accommodate a very largenumber of devices in extremely contested environments such that the collectionof all observations is reproduced at the destination with the best possiblefidelity. We formulate a remote estimation problem in the mean-field regimewhere a very large number of sensors communicate their observations to anaccess point, or base station, under a strict constraint on the maximumfraction of transmitting devices. We show that in the mean-field regime, thisproblem exhibits a structure that enables tractable optimization algorithms.More importantly, we obtain a data-driven learning scheme that admits a finitesample-complexity guarantee on the performance of the resulting estimationsystem under minimal assumptions on the data's probability density function.

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