Average Optimality for Adaptive Markov Control Processes with Unbounded Costs and Unknown Disturbance Distribution

Abstract

We study the adaptive control problem for a class of discrete-time Markov control processes with Borel state and action spaces, and possibly unbounded one-stage costs. The processes evolve according to recursive equations x t +1 = F(x t , a t ,ξ t ),t = 0, 1,…, with i.i.d. ℜ k — valued random vectors ξ t with unknown distribution. Assuming observability of ξ t , we propose three different sets of conditions each of which allows us to prove average optimality of a type of adaptive control policies.