[Feature Request] Add maximize flag to PosteriorMean acquisition function

[lukasfro]

Unlike other acquisition functions, the PosteriorMean does not have a maximize flag, hence it is not currently not possible to find the minimum of the posterior mean function via optimize_acqf. This should not be too much effort to implement. Happy to create a PR when the feature is desired.

[saitcakmak]

Hi @lukasfro. With the existing API, you can use

pm = PosteriorMean(model=model, objective=ScalarizedObjective(weights=torch.tensor([-1.0]))
optimize_acqf(...)

to minimize the posterior mean. This will internally negate the posterior, so any value you get out of this will also be negated.

You may have noticed that everything is maximized by default in BoTorch. If you need to minimize a function, it is typically easiest to just negate your function evaluations and maximize that. In the past, I worked with BoTorch in a minimization setting without negating the function evaluations and things get messy pretty quickly.

[lukasfro]

Hi @saitcakmak, thanks for the clarification. It looks like ScalarizedObjective is the way to go then. I thought it might be nice to have a consistent interface to the other analytical acquisition functions that do make use of the maximize flag.

[Balandat]

I think it would be fine to add a maximize arg to PosteriorMean for consistency with the other analytic acquisition functions. Should be trivial to do by adding a constructor and flipping a sign conditionally on that in forward. Happy to review a PR for this :)

[lukasfro]

Sounds good to me. Will create the PR next week!
I just noticed that ScalarizedPosteriorMean could be extended in a similar manner. Should this be included in the PR as well?

[Balandat]

I don't think ScalarizedPosteriorMean needs a maximize option, since this can easily be done just by flipping the sign of the weights.

[Balandat]

For PosteriorMean, this was added by #881.