This paper investigates the problem of efficient constrained global optimization of composite functions (hybrid models) whose input is an expensive black-box function with vector-valued outputs and noisy observations, which often arises in real-world science, engineering, manufacturing, and control applications. We propose a novel algorithm, Constrained Upper Quantile Bound (CUQB), to solve such problems that directly exploits the composite structure of the objective and constraint functions that we show leads substantially improved sampling efficiency. CUQB is conceptually simple and avoids the constraint approximations used by previous methods. Although the CUQB acquisition function is not available in closed form, we propose a novel differentiable stochastic approximation that enables it to be efficiently maximized. We further derive bounds on the cumulative regret and constraint violation. Since these bounds depend sublinearly on the number of iterations under some regularity assumptions, we establish explicit bounds on the convergence rate to the optimal solution of the original constrained problem. In contrast to existing methods, CUQB further incorporates a simple infeasibility detection scheme, which we prove triggers in a finite number of iterations (with high probability) when the original problem is infeasible. Numerical experiments on several test problems, including environmental model calibration and real-time reactor optimization, show that CUQB significantly outperforms traditional Bayesian optimization in both constrained and unconstrained cases. Furthermore, compared to other state-of-the-art methods that exploit composite structure, CUQB achieves competitive empirical performance while also providing substantially improved theoretical guarantees.

翻译：本文研究复合函数（混合模型）的高效约束全局优化问题，其输入为具有向量值输出和含噪观测的昂贵黑箱函数。此类问题广泛存在于现实世界的科学、工程、制造及控制应用中。我们提出一种新型算法——约束上分位数界（CUQB），该算法直接利用目标函数与约束函数的复合结构，显著提升采样效率。CUQB概念简洁，避免了先前方法所使用的约束近似。尽管CUQB采集函数不存在闭式解，我们提出一种新型可微随机逼近方法，使其能够被高效最大化。进一步地，我们推导了累积遗憾与约束违反的界。在特定正则性假设下，这些界随迭代次数呈次线性增长，从而建立了原始约束问题最优解收敛速度的显式界。与现有方法不同，CUQB还引入一种简单的不可行性检测机制，我们证明当原始问题不可行时，该机制以高概率在有限迭代次数内触发。在包含环境模型校准和实时反应器优化等多个测试问题的数值实验中，CUQB在约束与无约束情形下均显著优于传统贝叶斯优化。此外，与其他利用复合结构的先进方法相比，CUQB在取得竞争性经验性能的同时，提供了显著更优的理论保证。