Finite approximations in discrete-time stochastic control quantized models and asymptotic optimality introduction and summary

Abstract

Control and optimization of dynamical systems in the presence of stochastic uncertainty is a mature field with a large range of applications. A comprehensive treatment of such problems can be found in excellent books and other resources including [7, 16, 29, 68, 84, 95, 104], and [6]. To date, there exist a nearly complete theory regarding the existence and structure of optimal solutions under various formulations as well as computational methods to obtain such optimal solutions for problems with finite state and control spaces. However, there still exist substantial computational challenges involving problems with large state and action spaces, such as standard Borel spaces. For such state and action spaces, obtaining optimal policies is in general computationally infeasible.