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.

翻译：现实世界中存在大量需要同时优化多个准则的黑箱优化问题。然而，在多目标优化（MOO）问题中，识别整个帕累托前沿需要高昂的搜索代价，而在许多实际场景中，决策者（DM）仅需从帕累托最优解集中获取特定解。我们提出一种贝叶斯优化（BO）方法，用于在目标函数评估代价高昂的MOO中识别最偏好的解，该方法通过交互方式基于两类监督信息——成对偏好与改进请求——自适应地估计DM的贝叶斯偏好模型。为探索最偏好的解，我们定义了一个采集函数，该函数同时融合了目标函数与DM偏好的不确定性。此外，为最小化与DM的交互成本，我们还提出一种针对偏好估计的主动学习策略。通过基准函数优化及机器学习模型的超参数优化问题，我们实证验证了所提方法的有效性。