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Fix PosteriorMeanModel and add qPosteriorMean/qPosteriorStandardDeviation acquisition functions #2634

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Motivation

This is a small collection of changes for improving support for optimisation with deterministic (posterior mean) and pure exploration (posterior std) acquisition functions:

  1. Using PosteriorMeanModel with optimize_acqf is currently not supported as PosteriorMeanModel does not implement num_outputs or batch_shape.
  2. The PosteriorMean and PosteriorStandardDeviation acquisition functions have no MC equivalent.

This PR addresses the points above, and consequentially adds support for the constrained PSTD acquisition function.

Have you read the Contributing Guidelines on pull requests?

Yes

Test Plan

TODO - just submitting draft for now for discussion.

Related PRs

(If this PR adds or changes functionality, please take some time to update the docs at https://github.com/pytorch/botorch, and link to your PR here.)

@facebook-github-bot facebook-github-bot added the CLA Signed Do not delete this pull request or issue due to inactivity. label Nov 20, 2024
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