  We address the problem of minimizing the long-run expected average cost of a
complex system consisting of interactive subsystems. We formulate a
multiobjective optimization problem of the one-stage expected costs of the
subsystems and provide a duality framework to prove that the control policy
yielding the Pareto optimal solution minimizes the average cost criterion of
the system. We provide the conditions of existence and a geometric
interpretation of the solution. For practical situations with constraints
consistent to those studied here, our results imply that the Pareto control
policy may be of value when we seek to derive online the optimal control policy
in complex systems.
