非平稳MDP平均模型—状态空间可数情形

NO-STATIONARY MDP MODEL WITH THE AVERAGE CRITERION—THE DENUMERABLE STATE SPACE CASE

本文利用扩充的不动点定理,建立了相应于非平稳MDP平均模型的最优方程,据此给出了最优策略和ε-最优策略存在的充分条件.许多有关平稳MDP平均模型的结果,尤其是Ross(1983)的结果,均可由本文给出.

In this paper,using the generalization of the fixed point theorem for cont-ractions,we set up the optimal equation for non-stationary MDP with the aver-age criterion and supply the sufficent conditions under which either the optimalor ε-optimal polices exists.Many results for stationary MDP model with theaverage criterion,especially the results obtained by Ross(1983),can be taken asthe typical example of this paper.