MOMENT OPTIMAL MODELS FOR DISCRETE TIME MARKOV DECISION PROCESSES WITH DISCOUNT DEPENDING ON HISTORIES

Moment optimal models for discrete-time MDP with discount depending on histories, with countable state and aetion spaces are established. Some general form ulas of the k-th moment of discounted total return are given under various policy clases. The structure and some properties of moment optimal polioies are disoussed. It is shown that there exists a unique bounded solution for the momont optimal functional equation under some condi-tions.