The book includes an annotated bibliography outlining successes in a wide range of areas spanning science and engineering.

bayesian optimisation can be used in cases where gradient evaluation is expensive. in neural networks this can be applied to selecting hyper-parrameters to a trained model

There are other gradient free optimizers (like Powell's method) that are simpler and in my experience work better.

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?

bayesian methods are also prefered due to their well understood theoretical properies. this is one of the things you really want when you build safety critical models

I'm having a hard time imagining how using Bayesian optimization would improve safety during the search process, especially since in practice it often tends to just give approximately uniform sampling of a space anyway. It really likes the unexplored territory and is likely to try things far away from the optimum that are more risky.

Some research has explicitly considered the question of safety during exploration; see for example https://arxiv.org/pdf/1602.04450.pdf which includes theoretical analysis of the resulting algorithm.

Interesting, although the existence of this research actually suggests that normal Bayesian opt by itself is not safe and needs to be modified to be so.

A relatively unique trait of Bayesian opt is the modelling of unexplored space. The attraction to exploring that space makes it actually less safe than other methods that do not explicitly care.

One could go through similar steps to model and generate safe steps in other methods. It doesn't seem specific to Bayesian opt. It might even be better since it's less likely to be so computationally expensive as the auxiliary opt within Bayesian opt tends to be.

Indeed -- safety in exploration is not a relevant concern in all (or even in most) scenarios. However, in domains such as robotics where certain configurations may have unforeseen and severe consequences, you may want to slow down exploration and proceed more cautiously. As you suggest, you can optimize more efficiently if you can explore the domain without any safety concerns.

You're correct that the approach taken in the linked paper could be adapted to increase the safety of other sequential design settings (when needed), assuming you have access to a model that can quantify uncertainty.

i mean it in terms of explainability. the point is that bayesian methods can be used to investigate theoretical properties of machine learning models that might otherwise be opaque. they can also provide estimates of model-uncertainty