Optimal adaptive policies for Markov decision processes

In this paper we consider the problem of adaptive control for Markov Decision Processes. We give the explicit form for a class of adaptive policies that possess optimal increase rate properties for the the total expected finite horizon reward, under sufficient assumptions of finite state-action spaces and irreducibility of the transition law. A main feature of the proposed policies is that the choice of actions, at each state and time period, is based on indices that are inflations of the right-hand side of the estimated average reward optimality equations.