Adaptive control for discrete-time Markov processes with unbounded costs: Average criterion

The paper deals with a class of discrete-time Markov control processes with Borel state and action spaces, and possibly unbounded one-stage costs. The processes are given by recurrent equations x <Subscript> t </Subscript> <Subscript>+1</Subscript>=F(x <Subscript> t </Subscript>,a <Subscript> t </Subscript>,ξ<Subscript> t </Subscript>), t=1,2,… with i.i.d. ℜ<Superscript> k </Superscript>– valued random vectors ξ<Subscript> t </Subscript> whose density ρ is unknown. Assuming observability of ξ<Subscript> t </Subscript>, and taking advantage of the procedure of statistical estimation of ρ used in a previous work by authors, we construct an average cost optimal adaptive policy. Copyright Springer-Verlag Berlin Heidelberg 1998