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：部分可观测约束优化问题（POCOPs）阻碍了数据驱动优化技术的发展，因为POCOPs的不可行解几乎无法提供关于目标函数和约束条件的有用信息。我们致力于在约束贝叶斯优化框架下，为昂贵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，我们改进了采集函数的设计，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以证明其有效性。其次，我们提出一种嵌入不同似然函数的高斯过程作为部分可观测约束的代理模型。与传统基于分类的模型相比，该模型能更精确地刻画可行区域。通过合成问题与实际问题的实验研究，验证了所提方法在求解POCOPs问题上的竞争力。