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.