Abstract
A new mathematical model, which is called probabilistic Boolean networks (PBNs), has been developed to model complex genetic regulatory networks during the past decade. An important problem is to find optimal policies for a PBN so as to avoid undesirable states. Although several models of discrete time Markov decision processes (DTMDPs) have been applied to find optimal control policies, the existing literatures show that the objective functions focus on the long term and short term expected rewards/costs. Compared with previous works, a probability criterion for DTMDPs has been proposed to make the dynamic comparison of different treatment in the framework of PBNs. More precisely, this paper concentrates on the probability that the total loss incurred before the network first visit to desirable states. The application of our approach is also exhibited via two numerical examples.
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