AcqFunctionThompsonSampling

[jakob-r]

The AcqFun would be one sample of a gaussian process. Also nice for parallelization.

[sumny]

Add AcqFunctionThompsonSampling.
As a starting point for Acquisition Functions in general see R/AcqFunctionEI.R and tests/testthat/test_AcqFunctionEI.R.
For some background on simple sequential Thompson Sampling see Algorithm 1 in http://proceedings.mlr.press/v84/kandasamy18a/kandasamy18a.pdf.
We always assume that the posterior is multivariate gaussian (regardless of what kind of surrogate we are using).
For some more info see http://num.pyro.ai/en/stable/examples/thompson_sampling.html.

[sumny]

Some more clarification:
We cannot assume that we always use a GP as surrogate model that would allow us to get a mean and covariance prediction (and the current infrastructure only returns a mean an sd prediction anyhow).
Therefore, we should actually implement so-called independent Thompson sampling, see e.g. formula 5.5 here.