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This paper investigates the problem of efficient constrained globaloptimization of hybrid models that are a composition of a known white-boxfunction and an expensive multi-output black-box function subject to noisyobservations, which often arises in real-world science and engineeringapplications. We propose a novel method, Constrained Upper Quantile Bound(CUQB), to solve such problems that directly exploits the composite structureof the objective and constraint functions that we show leads substantiallyimproved sampling efficiency. CUQB is a conceptually simple, deterministicapproach that avoid constraint approximations used by previous methods.Although the CUQB acquisition function is not available in closed form, wepropose a novel differentiable sample average approximation that enables it tobe efficiently maximized. We further derive bounds on the cumulative regret andconstraint violation under a non-parametric Bayesian representation of theblack-box function. Since these bounds depend sublinearly on the number ofiterations under some regularity assumptions, we establis bounds on theconvergence rate to the optimal solution of the original constrained problem.In contrast to most existing methods, CUQB further incorporates a simpleinfeasibility detection scheme, which we prove triggers in a finite number ofiterations when the original problem is infeasible (with high probability giventhe Bayesian model). Numerical experiments on several test problems, includingenvironmental model calibration and real-time optimization of a reactor system,show that CUQB significantly outperforms traditional Bayesian optimization inboth constrained and unconstrained cases. Furthermore, compared to otherstate-of-the-art methods that exploit composite structure, CUQB achievescompetitive empirical performance while also providing substantially improvedtheoretical guarantees.

No-Regret Constrained Bayesian Optimization of Noisy and Expensive Hybrid Models using Differentiable Quantile Function Approximations