We address the problem of minimizing the long-run expected average cost of acomplex system consisting of interactive subsystems. We formulate amultiobjective optimization problem of the one-stage expected costs of thesubsystems and provide a duality framework to prove that the control policyyielding the Pareto optimal solution minimizes the average cost criterion ofthe system. We provide the conditions of existence and a geometricinterpretation of the solution. For practical situations with constraintsconsistent to those studied here, our results imply that the Pareto controlpolicy may be of value when we seek to derive online the optimal control policyin complex systems.
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