Allow TRs to be created with empty/single region

[khurram-ghani]

Related issue(s)/PRs: None

Summary

This PR updates batch trust-region classes to allow init_subspaces to be empty. The request came from this discussion. Default subspaces are created if init_subspaces is None, with the number of spaces equal to the batch_size/num_query_points in the base rule.

Unfortunately, there is no mechanism or concept in the base AcquistionRule for batch size. So this PR uses the dynamic type of the base rule, with current support for EfficientGlobalOptimization.

This PR also allows users to specify a single init-subspace more easily. That is, init_subspaces can now be None, a single value or a sequence.

Fully backwards compatible: yes

PR checklist

• The quality checks are all passing
• The bug case / new feature is covered by tests
• Any new features are well-documented (in docstrings or notebooks)

[vpicheny]

naive question: why is initialisation done here and not within __init__?

[khurram-ghani]

It is because the subspaces we have (e.g. SingleObjectiveTrustRegionBox) need the global search space at initialisation time; which is not available in the rule __init__. I could have added it there as a required argument, but since that is already provided to acquire, I deferred that creation till then.

Note this does raise an important point. The subspaces take the reference to the global search space once (e.g. in first call to acquire). Theoretically the users can change the global search space to subsequent calls to acquire, but that would be ignored. I don't know how other rules deal with that or if that is even valid.

[vpicheny]

That makes sense!

Regarding the second point, if you change the global search space, then your trust region may become invalid. In that case it would make sense for the user to manually re-initialise it.

I guess we could either assert that the spaces match at every acquire call, or just ignore this corner case?

[khurram-ghani]

For the case where users create the subspaces outside the class, the global search space passed to acquire is completely ignored -- it is only used for this default initialisation case. So the full strict check check would be to assert the search space in every call to acquire is equal to the one stored inside every subspace. I hope that check is not too restrictive. I'll go ahead and add that.