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expensive black-box functions

Expensive black-box functions are mathematical or computational processes whose internal formulas and gradient information are unknown or inaccessible, and where each individual evaluation incurs a substantial cost in time, computational effort, or physical resources. In such systems, which frequently appear in complex computer simulations, physical experimentation, and algorithm parameter tuning, an observer can only provide an input and measure the resulting output without inspecting the underlying analytical structure. Because evaluating the function is resource-intensive, the total budget for queries is strictly limited, making traditional gradient-based or exhaustive search techniques impractical. As a result, optimizing or analyzing these functions typically relies on sample-efficient strategies, such as surrogate modeling and Bayesian optimization, which approximate the function landscape from a small set of evaluations while systematically balancing the exploration of uncertain regions with the exploitation of promising areas.

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Constrained Efficient Global Optimization of Expensive Black-box Functions

Wenjie Xu, Yuning Jiang, Bratislav Svetozarevic, Colin N. Jones

OrganizationsGeneral Motors Research LaboratoriesNational Institute of Statistical SciencesUniversity of Waterloo

Why you should read this

Introduces the Efficient Global Optimization (EGO) algorithm using Kriging-based stochastic process models and expected improvement to find global optima of expensive black-box functions with minimal evaluations.

In many engineering optimization problems, the number of function evaluations is severely limited by time or cost. These problems pose a special challenge to the field of global optimization, since existing methods often require more function evaluations than can be comfortably afforded. One way to address this challenge is to fit response surfaces to data collected by evaluating the objective and constraint functions at a few points. These surfaces can then be used for visualization, tradeoff analysis, and optimization. In this paper, we introduce the reader to a response surface methodology that is especially good at modeling the nonlinear, multimodal functions that often occur in engineering. We then show how these approximating functions can be used to construct an efficient global optimization algorithm with a credible stopping rule. The key to using response surfaces for global optimization lies in balancing the need to exploit the approximating surface (by sampling where it is minimized) with the need to improve the approximation (by sampling where prediction error may be high). Striking this balance requires solving certain auxiliary problems which have previously been considered intractable, but we show how these computational obstacles can be overcome.

Added

2026-09-18