Comparison of acquisition functions in bayesian optimization

From what i can see from various references, they said that expected improvement is most commonly used compared with other acquisition functions, such as probability of improvement and LCB (in-built function in matlab). Why is that so? (Concept question)

Answer 1

[Alan Weiss]

I am not an expert in this area, but I'll tell you what I know about acquisition function types. From what I understand, in internal testing it was found that 'expected-improvement-per-second-plus' (default) works well; the 'per second' attribute allows for faster model-building and optimization in some ways, and the 'plus' attribute avoids overexploiting an area (more search for a global minimum). The "probability of improvement" calculation does not take into account the amount of improvement, so is a simpler model, and as such I would expect it to do worse on reasonably smooth or predictable problems. The "lower confidence bound" is another function that ignores much information about a problem, so should perform worse when the problem is predictable or smooth. Conversely, if you have a very noisy or unpredictable problem, then maybe these insensitive acquisition functions would be more appropriate.

Just my 2 cents, I'm sure that an expert can give you more information.

Alan Weiss

MATLAB mathematical toolbox documentation