Noisy optimization

[icouckuy]

This issue keeps track of the support for stochastic optimization. In machine learning the standard expected improvement is often used, which actually does not account for possible noise.

As a first step we are looking at implementing the augmented EI or a variation thereof as described in:
https://hal.archives-ouvertes.fr/hal-00658212/document

[javdrher]

Right now we implement (17) in that paper. We could add (18), should not be a big problem,

[javdrher]

(18) is implemented in the notebook on defining new acquisition functions. We won't be adding it to the library as a standard option though. In case someone wants to try other options, the framework allows implementation

In the project proposal we added the knowledge gradient. This would be an included algorithm supporting noisy objectives.