Benchmark BoTorch Acquisition Functions

[ghutchis]

For now, the code uses UCB with a formula favoring increasing exploration, which might make sense for finding all minima.

Benchmark # of steps required and lowest minima across a subset of the BOKEI test set:

• [X] UCB
• [x] Expected Improvement
• [x] log Expected Improvement
• [ ] Probability of Improvement
• [ ] log Probability of Improvement

Other interesting acquisition functions in BoTorch:

• [ ] noisy EI (should be similar to EI, but worth checking)
• [ ] q-variants to analytic acquisition functions
• [ ] SAASBO
• [ ] GIBBON
• [ ] Knowledge gradient (botorch.acquisition.knowledge_gradient.qKnowledgeGradient)
• [ ] Entropy Search (MES) (botorch.acquisition.max_value_entropy_search.qMaxValueEntropy)

[ghutchis]

botorch expected improvement methods don't give the $\epsilon$ hyper parameter to push for more exploration.

It might be worth modifying the "best value" (e.g., best + 0.01) to push for more exploration like with the current UCB method.