A comparison study of optimal and suboptimal intervention policies for gene regulatory networks in the presence of uncertainty

Perfect knowledge of the underlying state transition probabilities is necessary for designing an optimal intervention strategy for a given Markovian genetic regulatory network. However, in many practical situations, the complex nature of the network and/or identification costs limit the availability of such perfect knowledge. To address this difficulty, we propose to take a Bayesian approach and represent the system of interest as an uncertainty class of several models, each assigned some probability, which reflects our prior knowledge about the system. We define the objective function to be the expected cost relative to the probability distribution over the uncertainty class and formulate an optimal Bayesian robust intervention policy minimizing this cost function. The resulting policy may not be optimal for a fixed element within the uncertainty class, but it is optimal when averaged across the uncertainly class. Furthermore, starting from a prior probability distribution over the uncertainty class and collecting samples from the process over time, one can update the prior distribution to a posterior and find the corresponding optimal Bayesian robust policy relative to the posterior distribution. Therefore, the optimal intervention policy is essentially nonstationary and adaptive.