Partially observable Markov control models with random discount factors

Abstract

Three elements are needed to define an optimal control problem (OCP): (1) a decision or control model; (2) a set of admissible control policies, and (3) a performance index. So, the OCP is to find a control policy that minimizes the performance index. We can classify the OCPs in a variety of ways, for instance: deterministic or stochastic; continuous or discrete time; finite or infinite horizon; discounted or average cost performance index; with partial or complete state-system information, among others. In this work we focus on the study of OCPs considering partially observable discrete-time stochastic systems, under a discounted optimality criterion, but unlike the standard case, we assume random discount factors.