Adaptive policies for discrete-time stochastic control systems with unknown disturbance distribution

Abstract

We introduce adaptive policies for discrete-time, infinite horizon, stochastic control systems x 1+1 = F( x 1, a 1, ξ 1, t =0, 1, …, with discounted reward criterion, where the disturbance process ξ 1 is a sequence of i.i.d. random elements with unknown distribution. These policies are shown to be asymptotically optimal and for each of them we obtain (almost surely) uniform approximations of the optimal reward function.