Black Box Bayesian Optimization

What is black box optimization?

Black box optimization (BBO) refers to a scenario in which we have a function that we want to optimize, but have little to no information about its internal structure, such as its derivatives or explicit mathematical form. This is a common situation in many real-world optimization problems, where the function might be computationally expensive or involve complex simulations.

For example, we want to know the relationship between the number of products a machine produces to the number of hours it works. We consider this an ideal state where every piece of information is known so we can create this optimization problem in a simple linear manner. This is shown below: