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 xt+1 = F(xt,at,ξt), t = 1, 2, ... with independent, identically distributed ℜ^k-valued random vectors ξt whose density p is unknown. Assuming observability of ξt, and taking advantage of the procedure of statistical estimation of p used in a previous work by the authors, we construct an average cost optimal adaptive policy.