Borel状态空间非平稳MDP的平均方差准则

本文考虑具有 Ｂｏｒｅｌ状态空间和行动空间非平稳 ＭＤＰ的平均方差准则．首先，在遍历条件下，利用最优方程，证明了关于平均期望目标最优马氏策略的存在性．然后，通过构造新的模型，利用马氏过程的理论，进一步证明了在关于平均期望目标是最优的一类马氏策略中，存在一个马氏策略使得平均方差达到最小．作为本文的特例还得到了 Ｄｙｎｋｉｎ Ｅ． Ｂ．和 Ｙｕｓｈｋｅｖｉｃｈ Ａ． Ａ．及 Ｋｕｒａｎｏ Ｍ．等中的主要结果．

The Average Variance Criterion for Nonstationary MDP with Borel State Space

In this paper, we consider the average variance criterion for nonstationary Markov decision processes (MDP) with Borel state space. First, from the optimality equations we prove the existence of optimal Markov policies under ergodic conditions. Secondly, by the theory on Markov processes and structuring a new model we also prove that there exists a Markov policy, which is optimal in an average expected criterion, minimizes the average variance in the class of optimal policies for average expected criterion. So we extend the main results obtained by Dynkin E. B. and Yushkevich A. A. and by Kurano M. etc.