On Dynamic Programming and Statistical Decision Theory

Abstract

The main aim of the present work is to establish connections between the theory of dynamic programming and the statistical decision theory. The paper deals with a nonMarkovian dynamic programming decision model that includes Markovian decision models and Markov renewal decision models as special cases. The analysis is based on the total cost criterion where the convergence condition on the expected total cost is such that the discounted and the negative (unbounded) case are included. The striking feature of the present model is the fact that the law of motion is not completely known, which leads to a treatment of the model by the approach of statistical decision theory. The assumptions of the present paper are discussed for a sequential statistical decision problem.