Estimation and control in finite Markov decision processes with the average reward criterion
Volume 31 / 2004
Applicationes Mathematicae 31 (2004), 127-154
MSC: Primary 90C40, 93E20; Secondary 60J05.
DOI: 10.4064/am31-2-1
Abstract
This work concerns Markov decision chains with finite state and action sets. The transition law satisfies the simultaneous Doeblin condition but is unknown to the controller, and the problem of determining an optimal adaptive policy with respect to the average reward criterion is addressed. A subset of policies is identified so that, when the system evolves under a policy in that class, the frequency estimators of the transition law are consistent on an essential set of admissible state-action pairs, and the non-stationary value iteration scheme is used to select an optimal adaptive policy within that family.
