离散时间MDP矩最优模型——折扣依赖于历史的情形

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

本文在S、A(i)(i∈S)均匀可列集情形下,建立了折扣依赖于历史的矩最优模型。给出了折扣总报酬k阶矩在各类策略下的统一表达式;讨论了矩最优策略的结构与性质;证明了矩最优方程在给定条件下,存在唯一的有界解。

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.