Personalized Bayesian optimization for noisy problems

In many real-world applications of interest, several related optimization tasks can be encountered, where each task is associated with a specific context or personalized information. Moreover, the amount of available data for each task may be highly limited due to the expensive cost involved. Although Bayesian optimization (BO) has emerged as a promising paradigm for handling black-box optimization problems, addressing such a sequence of optimization tasks can be intractable due to the cold start issues in BO. The key challenge is to speed up the optimization by leveraging the transferable information, while taking the personalization into consideration. In this paper, optimization problems with personalized variables are formally defined at first. Subsequently, a personalized evolutionary Bayesian algorithm is proposed to consider the personalized information and the measurement noise. Specifically, a contextual Gaussian process is used to jointly learn a surrogate model in different contexts with regard to the varying personalized parameter, and an evolutionary algorithm is tailored for optimizing an acquisition function for handling the presence of personalized information. Finally, we demonstrate the effectiveness of the proposed algorithm by testing it on widely used single- and multi-objective benchmark problems with personalized variables.