MCMC hyperparameter marginalization

[Joachim van der Herten]

Rather than only relying on point-estimates for the hyperparameters, we should include the ability to average the acquisition scores over several draws from the log likelihood + log prior. This should not be too hard to accomplish given the support to sum acquisitions, and the MCMC support built in GPflow. What I had in mind:

1. Include an option for BayesianOptimizer to indicate the number of draws (n)
2. Copy the acquisition n times and sum them all together. This sum acquisition will then be optimized to select new sampling decisions
3. Each iteration, request all models of one of original acquisition object. Call sample on each model to obtain n draws. Then visit each acquisition of the sum and call set_state() on the models.

These steps only require limited changes in BayesianOptimizer. Two issues currently prevent implementation

1. When copying an acquisition object (and its underlying models) the order of sorted_params can change. This means calling set_state() with a free state vector obtained from another copy can have the wrong order. GPflow/GPflow#417 would solve this if merged
2. Right now, ei + ei + ei results in a tree structure, it would simpler if it results in some form of AggregateAcquisition which concatenates the scores and applies tf.reduce_sum. This would reduce the size of the tree and the TensorFlow graph, and is more efficient (I guess). This would require some additional code: I'm playing around with this right now and it seems to be straightforward.

[Joachim van der Herten]

Both issues were addressed, started working on this.

[Joachim van der Herten]

#31 implements the MCMC hyperparameter marginalization.