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. Code available at: https://github.com/yunshengtian/BE-CBO

翻译：贝叶斯优化已被成功应用于评估次数严重受限的黑箱函数优化问题。然而在许多实际应用中，由于物理或系统限制，设计方案的可行性往往难以预先判定。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。本文观察到，在此类场景中最优解通常位于设计空间可行域与不可行域的边界上，这比内点最优解问题难度显著增大。受此启发，我们提出BE-CBO——一种能有效探索可行与不可行设计边界的新型贝叶斯优化方法。为了识别边界，我们采用神经网络集成学习约束条件，该集成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证明，我们的方法性能超越当前最优方法。代码开源地址：https://github.com/yunshengtian/BE-CBO