Support batched sampling with BoTorch

[kstoneriv3]

Motivation

Currently, botorch integration of Optuna does not take the running trials into account when calculating the acquisition function. (By the way, in contrast, TPE has the constant_lier option that tries to leverage the information of running trials.) However, the original botorch API can leverage this information, and that seems to substantially improve parallel optimization performance.

On a simple benchmark using 10-dimensional quadratic function (y = sum_{i=0, ..., 9} |x_i|^2 with -5 <= x_i <= 5), with n_trials = 40 and n_workers=10, the average objective values were 4.55 ± 0.22 (w/ batching) vs 10.30 ± 0.59 (w/o batching). The script for the benchmark can be found at https://gist.github.com/kstoneriv3/1e877830e535d9ebea0f9d55ed50734c.

Description of the changes

I just need to change several lines of code at optuna.integration.botorch for passing the information about running trials to the BoTorch API. The test is WIP.

[contramundum53]

Changing the signature of candidates_func is considered a breaking change.

I personally think that it is OK because 1. BoTorchSampler itself is experimental, 2. not many people seem to be using customized candidates_func, and 3. for those people who do customize candidates_func, it is very easy to fix.

But it needs to be discussed.

It is also possible to avoid breaking change by adding a try/catch or a condition on calling candidates_func. (Although I think it's a bit of over-engineering.)

[kstoneriv3]

Thank you for the preliminary review! I added a test so the PR is ready for review.

[codecov-commenter]

Codecov Report

Merging #4591 (e178de8) into master (41045ce) will increase coverage by 0.01%.
The diff coverage is 95.23%.

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@@            Coverage Diff             @@
##           master    #4591      +/-   ##
==========================================
+ Coverage   90.88%   90.89%   +0.01%     
==========================================
  Files         184      184              
  Lines       13959    13983      +24     
==========================================
+ Hits        12686    12710      +24     
  Misses       1273     1273              

Impacted Files	Coverage Δ
optuna/integration/botorch.py	96.01% <95.23%> (+0.37%)	⬆️

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[kstoneriv3]

Following the comment by @contramundum53, I added a commit that would ensure backward compatibility. As discussed above, it seems to be a bit of overengineering and makes sample_relative even bigger. Please let me know whether you would like to keep it or not.

If you are happy with the current implementation, I will add an additional test for checking the backward compatibility and warning.

[github-actions]

This pull request has not seen any recent activity.

[HideakiImamura]

Thanks for the update. I have several comments. PTAL.

[contramundum53]

Sorry for my late reply 🙇
I added some comments.

[kstoneriv3]

Thank you for the review! I should have addressed all of your reviews. PTAL

[contramundum53]

LGTM! Thanks for the PR!

[HideakiImamura]

LGTM.