Bayesian optimization has been successfully applied to optimize black-box functions where the number of evaluations is severely limited. However, in many real-world applications, it is hard or impossible to know in advance which designs are feasible due to some physical or system limitations. These issues lead to an even more challenging problem of optimizing an unknown function with unknown constraints. In this paper, we observe that in such scenarios optimal solution typically lies on the boundary between feasible and infeasible regions of the design space, making it considerably more difficult than that with interior optima. Inspired by this observation, we propose BE-CBO, a new Bayesian optimization method that efficiently explores the boundary between feasible and infeasible designs. To identify the boundary, we learn the constraints with an ensemble of neural networks that outperform the standard Gaussian Processes for capturing complex boundaries. Our method demonstrates superior performance against state-of-the-art methods through comprehensive experiments on synthetic and real-world benchmarks.

翻译：贝叶斯优化已成功应用于评估次数严重受限的黑箱函数优化问题。然而在实际应用中，由于物理或系统限制，设计方案的可行性往往难以或无法预先获知。这导致了一个更具挑战性的问题：在未知约束条件下优化未知函数。本文发现，在此类场景中最优解通常位于设计空间可行域与非可行域的边界上，其求解难度远高于内部最优解问题。受此启发，我们提出BE-CBO——一种高效探索可行与非可行设计边界的贝叶斯优化新方法。为识别边界，我们采用神经网络集成学习约束条件，该方法在捕捉复杂边界时优于标准高斯过程。通过在合成基准和真实世界基准上的全面实验，我们的方法展现出优于现有最优方法的性能表现。