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

Abstract

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 t +1=F(x t ,a t ,ξ t ), t=1,2,… with i.i.d. ℜ k – valued random vectors ξ t whose density ρ is unknown. Assuming observability of ξ t , 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.