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Bayesian optimization (BO) is a framework for global optimization ofexpensive-to-evaluate objective functions. Classical BO methods assume that theobjective function is a black box. However, internal information aboutobjective function computation is often available. For example, when optimizinga manufacturing line's throughput with simulation, we observe the number ofparts waiting at each workstation, in addition to the overall throughput.Recent BO methods leverage such internal information to dramatically improveperformance. We call these "grey-box" BO methods because they treat objectivecomputation as partially observable and even modifiable, blending the black-boxapproach with so-called "white-box" first-principles knowledge of objectivefunction computation. This tutorial describes these methods, focusing on BO ofcomposite objective functions, where one can observe and selectively evaluateindividual constituents that feed into the overall objective; andmulti-fidelity BO, where one can evaluate cheaper approximations of theobjective function by varying parameters of the evaluation oracle.

Thinking inside the box: A tutorial on grey-box Bayesian optimization