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The partially observable constrained optimization problems (POCOPs) impededata-driven optimization techniques since an infeasible solution of POCOPs canprovide little information about the objective as well as the constraints. Weendeavor to design an efficient and provable method for expensive POCOPs underthe framework of constrained Bayesian optimization. Our method consists of twokey components. Firstly, we present an improved design of the acquisitionfunctions that introduces balanced exploration during optimization. Werigorously study the convergence properties of this design to demonstrate itseffectiveness. Secondly, we propose a Gaussian process embedding differentlikelihoods as the surrogate model for a partially observable constraint. Thismodel leads to a more accurate representation of the feasible regions comparedto traditional classification-based models. Our proposed method is empiricallystudied on both synthetic and real-world problems. The results demonstrate thecompetitiveness of our method for solving POCOPs.

Constrained Bayesian Optimization Under Partial Observations: Balanced Improvements and Provable Convergence