Should "First Step" example of GPyOpt find minimum?

Question

"First Step" page from GPyOpt shows pretty image, which looks like a minimum, found by code above

Unfortunately, when I run the very same code, I get

or

i.e. vertical line very rarely goes to minimum.

Is this my misunderstanding, or the library doesn't work?

Answer 1

To be clear, the red function is not representing the likelihood of a minimum, but the likelihood of obtaining valuable information in the next acquisition. And how "value" is assigned to information depends on the acquisition strategy one adopts.

My guess would be that their plot was generated from a run that used acquisition_type='MPI' (Maximum Probability of Improvement), which would explain why the acquisition appears aggressively focused on searching in the region with the suspected minimum. Perhaps that used to be the default on the API when they generated those docs.

Currently, the default is acquisition_type='EI' (Expected Improvement), which is a little more careful about ruling out regions that have less information about them before focusing in on the minimal region. Hence, you're seeing acquisitions targeted to locations with large uncertainty bounds, which is perfectly reasonable.

In the end, the inferred function should still yield nearly identical predictions of the optimal function parameters. The predicted optimum is obtained with

myBopt.x_opt