Analysis of an adaptive control scheme for a partially observed controlled Markov chain

The authors consider an adaptive finite state controlled Markov chain with partial state information, motivated by a class of replacement problems. They present parameter estimation techniques based on the information available after actions that reset the state to a known value are taken. It is proved that the parameter estimates converge w.p.1 to the true (unknown) parameter, under the feedback structure induced by a certainty equivalent adaptive policy. It is shown that the adaptive policy is self-optimizing in a long-run average sense, for any (measurable) sequence of parameter estimates converging w.p.1 to the true parameter