Markov decision processes based optimal control policies for probabilistic boolean networks

This paper addresses the control formulation process for probabilistic boolean genetic networks. It is a major problem that has not been investigated enough yet. We argue that a monitoring stage is necessary after the control stage for providing guidance about the evolution of the investigated state. For this purpose, we developed methods for generating optimal control policies for each of the following five cases: finite control, infinite control, finite control-infinite monitoring, finite control-finite monitoring, and repeated finite control-finite monitoring. Our initial proposal was based on using action cost functions in the process. In this study, we propose Markov decision processes as an alternative to the action cost functions approach. We conducted experiments on two simple illustrative examples to demonstrate that the considered five cases are necessary, effective and really matter while developing optimal control policies; the obtained results are promising.