The partially observable constrained optimization problems (POCOPs) impede data-driven optimization techniques since an infeasible solution of POCOPs can provide little information about the objective as well as the constraints. We endeavor to design an efficient and provable method for expensive POCOPs under the framework of constrained Bayesian optimization. Our method consists of two key components. Firstly, we present an improved design of the acquisition functions that introduces balanced exploration during optimization. We rigorously study the convergence properties of this design to demonstrate its effectiveness. Secondly, we propose a Gaussian process embedding different likelihoods as the surrogate model for a partially observable constraint. This model leads to a more accurate representation of the feasible regions compared to traditional classification-based models. Our proposed method is empirically studied on both synthetic and real-world problems. The results demonstrate the competitiveness of our method for solving POCOPs.

翻译：部分观测约束优化问题（POCOPs）阻碍了数据驱动优化技术，因为POCOPs的不可行解无法提供关于目标及约束的有效信息。我们致力于在约束贝叶斯优化框架下，为昂贵的POCOPs设计一种高效且可证明的方法。该方法包含两个关键组成部分。首先，我们提出了一种改进的采集函数设计，在优化过程中引入平衡探索。我们严格研究了该设计的收敛性质，以证明其有效性。其次，针对部分观测约束，我们提出了一种嵌入不同似然的高斯过程替代模型。与传统基于分类的模型相比，该模型能更准确地表征可行域。我们通过合成问题与实际问题对所提方法进行了实证研究。结果表明，该方法在求解POCOPs方面具有竞争力。