离散时间马氏决策过程理论及在概率布尔网络中的应用

In this project, we study the theory and applications of discrete-time Markov decision processes. The first part is on the theory of discrete-time Markov decision processes. More precisely, we focus on the existence of optimal policies under risk probability criterion, and we also consider the efficient algorithm for computing optimal policies. The second part is on applications of Markov decision processes in probabilistic Boolean networks.The main contributions of applications of discrete-time Markov decision processes are concluded in the following aspects.(1)We solve an optimal control problem by choosing the probabilities of Boolean networks in a probabilistic Boolean networks. (2)We make use of the theory of discrete-time Markov decision processes to solve optimal control problems for probabilistic Boolean networks. The aims of this project are to promote further development of theoretical and applications studies on discrete-time Markov decision processes.

基于离散时间马氏决策过程理论和应用的新进展，本项目拟在已有工作基础上，对离散时间马氏决策过程理论和应用两方面展开研究。理论研究为探索离散时间马氏决策过程风险概率准则意义下最优策略存在的更一般的条件及其算法。应用研究主要包括：(1)研究概率布尔网络中每个布尔网络被选取的概率；(2)利用离散时间马氏决策过程建模，对概率布尔网络中的最优干预问题展开研究。完成本项目中的研究内容能将离散时间马氏决策过程理论和应用研究推向深入。

本项目主要集中于马氏决策过程应用方面的研究。研究内容主要包括：(1)研究概率布尔网络中每个布尔网络被选取的概率；(2)利用半马氏决策过程建模，对概率布尔网络中的最优干预问题展开研究。