Theory of Finite Horizon Markov Decision Processes

Abstract

In this chapter we will establish the theory of Markov Decision Processes with a finite time horizon and with general state and action spaces. Optimization problems of this kind can be solved by a backward induction algorithm. Since state and action space are arbitrary, we will impose a structure assumption on the problem in order to prove the validity of the backward induction and the existence of optimal policies. The chapter is organized as follows.