Information theory criteria for design space exploration

[ArnoStrouwen]

Taken from a discussion with @ludoro on SciML slack:

As an alternative to acquisition functions, such as expected improvement, information theory based criteria could be used to pick new points to evaluate the objective at. Such as Fisher information or Shannon information. Some of these methods are described in:
https://link.springer.com/chapter/10.1007/978-1-4939-8847-1_6
These information theory based methods have mostly been used to improve prediction variance over the entire design space, but recently they have also been used to find the maximum of the objective.
https://www.tandfonline.com/doi/abs/10.1080/16843703.2018.1542965

[atiyo]

To take this idea a bit further: the whole notion of efficient data acquisition for surrogates is essentially the same as active learning.From this perspective, one might dip into the active learning literature for a whole set of applicable techniques (including the information theoretic driven ones).

Edit: somehow submitted comment before I finished typing!

[ArnoStrouwen]

https://bayesoptbook.com/
Overview of many interesting techniques such as entropy search.