There are a lot of real-world black-box optimization problems that need to optimize multiple criteria simultaneously. However, in a multi-objective optimization (MOO) problem, identifying the whole Pareto front requires the prohibitive search cost, while in many practical scenarios, the decision maker (DM) only needs a specific solution among the set of the Pareto optimal solutions. We propose a Bayesian optimization (BO) approach to identifying the most preferred solution in the MOO with expensive objective functions, in which a Bayesian preference model of the DM is adaptively estimated by an interactive manner based on the two types of supervisions called the pairwise preference and improvement request. To explore the most preferred solution, we define an acquisition function in which the uncertainty both in the objective functions and the DM preference is incorporated. Further, to minimize the interaction cost with the DM, we also propose an active learning strategy for the preference estimation. We empirically demonstrate the effectiveness of our proposed method through the benchmark function optimization and the hyper-parameter optimization problems for machine learning models.

提出了一种贝叶斯优化方法，用于在具有昂贵目标函数的多目标优化问题中确定最优解，通过交互方式自适应地估计DM的贝叶斯偏好模型，并利用获得的偏好信息进行主动学习，从而有效地在基准函数优化和机器学习模型的超参数优化问题中找到最优解。

多目标主动偏好学习的贝叶斯优化