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A key issue in the control of distributed discrete systems modeled as Markovdecisions processes, is that often the state of the system is not directlyobservable at any single location in the system. The participants in thecontrol scheme must share information with one another regarding the state ofthe system in order to collectively make informed control decisions, but thisinformation sharing can be costly. Harnessing recent results from informationtheory regarding distributed function computation, in this paper we derive, forseveral information sharing model structures, the minimum amount of controlinformation that must be exchanged to enable local participants to derive thesame control decisions as an imaginary omniscient controller having fullknowledge of the global state. Incorporating consideration for this amount ofinformation that must be exchanged into the reward enables one to trade thecompeting objectives of minimizing this control information exchange andmaximizing the performance of the controller. An alternating optimizationframework is then provided to help find the efficient controllers and messagingschemes. A series of running examples from wireless resource allocationillustrate the ideas and design tradeoffs.

A Framework for Rate Efficient Control of Distributed Discrete Systems