Adaptive control of constrained Markov chains

Adaptive control of finite-state Markov chains is discussed, The optimal performance is characterized through the minimization of a long-run average cost functional, subject to constraints on several other such functionals. Under mild structural and feasibility conditions, two explicit adaptive control policies are exhibited for the case where the transition probabilities are unknown. The policies are optimal under the constrained optimization criterion. They rely on a powerful estimation scheme which provides consistent estimators for the transition probabilities. This scheme is of independent interest, as it provides strong consistency under a large number of adaptive schemes and is independent of any identifiability conditions. As an application, an optimal adaptive policy is derived for a system of K competing queues with countable state space, for which the constrained criteria arise naturally in the context of communication networks