Adaptive policies for stochastic systems under a randomized discounted cost criterion

The paper deals with a class of discrete-time stochastic control processes under a discounted optimality criterion with random discount rate, and possibly unbounded costs. The state process {x t} and the discount process {a t;} evolve according to the coupled difference equations x t/+i = F(x t,a tt,a tξ t), a t+1 = G(a t,n t) where the state and discount disturbance processes {ξ t} and {η t} are sequences of i.i.d. random variables with unknown distributions θξ and θ η" respectively. Assuming observability of the process {(St, ξ t)), we use the empirical estimator of its distribution to construct asymptotically discounted optimal policie.