I think of Bayes-opt as addressing multiple challenges: (a) the function being a black box, i.e. gradient info isn't available (b) tolerance to some level of noise - the author addresses this in one of his comments here (c) economic # of calls to the black box function because it might be expensive to evaluate (like in the case of hyperparameter optimization, where a function evaluation means retraining the model).

Powell's methods - COBYLA et al - address only (a) I think. But I might be wrong not having worked on them extensively. Do they also address the other challenges?