Bayesian Learning Based Optimization for Stochastic Logical System

Abstract

The optimization problem of stochastic logical systems is studied in this paper. To deal with a system without knowledge of the objective function, a Bayesian optimization framework is extended with the learning algorithm called Gaussian process. Firstly, the regret bound, which represents the difference between the true optimal value and the achieved objective function value, is evaluated with exploiting the statistic features of Gaussian process. A numerical example is illustrated for the purpose of validation on the optimization algorithm afterward.