Acquisition function API redesign

[till-m]

Redesign the way acquisition functions work.

Content:

• Deletes the UtilityFunction class and replaces it with a generic AcquisitionFunction base class
• Delete acq_max, let each acquisition function handle the maximization itself
• Adds UpperConfidenceBound, ProbabilityOfImprovement and ExpectedImprovement as possible utility functions
• Adds wrapper acquisition function GPHedge to find which of (a combination of) UCB/PoI/EI are best suited for a problem #439
• ~Adds wrapper acquisition function KrigingBeliever to allow for async optimization #347 #365~
• Adds wrapper acquisition function ConstantLiar to allow for async optimization #347 #365. Strategies are min, max, mean and constant (latter chosen by supplying a number).
• Disallow constrained optimization for UCB -- the constrained optimization relies on the acquisition function being lower-bounded by zero, otherwise the rescaling doesn't make so much sense. While the old implementation seems to have worked sufficiently well, this is more principled.
• ~Sets default unconstrained acquisition function to GPHedge with base functions UCB(kappa=2.576), PoI(xi=0.01), EI(xi=0.01).~ Sets default unconstrained acquisition function to UCB(kappa=2.576)
• ~Set GPHedge with base functions PoI(xi=0.01), EI(xi=0.01) as standard acquisition function for constrained improvement~ Sets default constrained acquisition function to EI(xi=0.01)
• Make the acquisition function a property of the optimizer (this should mean the the optimizer as a whole is serializable, including the acquisition function, though I haven't actually tested this). This change is breaking as it means suggest, maximize etc. don't take an acquisition function argument anymore.

Why? The old UtilityFunction and acq_max were the most inflexible part of this package and their design was somewhat convoluted (e.g. providing a xi parameter when using UCB). Now it should be much easier to add custom acquisition functions.

[codecov[bot]]

Codecov Report

All modified and coverable lines are covered by tests :white_check_mark:

Project coverage is 96.23%. Comparing base (f2c720e) to head (3d85734). Report is 1 commits behind head on master.

Additional details and impacted files

```diff @@ Coverage Diff @@ ## master #447 +/- ## ========================================== + Coverage 94.68% 96.23% +1.54% ========================================== Files 9 10 +1 Lines 677 849 +172 ========================================== + Hits 641 817 +176 + Misses 36 32 -4 ```

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[till-m]

Some more changes:

• Add ConstantLiar
• fix a bug in exploration_decay
• fix a bug in KrigingBeliever, where the GP was fitted on the wrong data
• Adapted the async_optimization.py script to showcase ConstantLiar
• Reran some notebooks

@fmfn @bwheelz36 @leandrobbraga I will wait with merging this until the docstrings are finished, but if you'd like to give some feedback already, please do. @pfebrer this contains GPHedge, if you'd like to give some feedback on it. @rizhiy I added the constant liar and the kriging believer for async optimization, as well as a script based on your code in examples/async_optimization_dummies.py. Ideally this will eventually become a notebook. According to this, lying is the better strategy, but I wasn't sure whether it would make sense for constrained optimization, so I added the believer for that case.

[bwheelz36]

Wow this is a huge amount of work. Impressive! Before we start review can you resolve the merge conflicts and make sure all the tests pass?

[till-m]

Before we start review can you resolve the merge conflicts and make sure all the tests pass?

Will do 👍 ideally I want to wait until the docs are finished to only deal with one conflict. After that I will mark the PR as ready to review :)

[bwheelz36]

@till-m - will be a breaking redesign? Not necessarily against it, just want to be clear.

[till-m]

@till-m - will be a breaking redesign? Not necessarily against it, just want to be clear.

There will be some necessary breaking changes, primarily to workflows that change the acquisition function -- this is unavoidable, since the old UtilityFunction object has been replaced. I also (intentionally) modified the way the acquisition function is changed -- it is now a property of the optimizer (i.e. not an argument to maximize/suggest). I understand that this can be annoying for some users, but I think in the long run it will be exactly those users that will profit from this change.

If someone just calls .maximize nothing should change. Similarly, suggest-probe-register w/o messing with the acquisition function will not change either.

[till-m]

@bwheelz36 I know this is a lot. I'm sorry about that 😬

[till-m]

Coverage is fixed now! :)

Agree on all other points. Thanks for the review! :)