Acquisition Function to optimize Matheron Path Samples

[jduerholt]

Hi all,

I have a question regarding Thompson sampling with Matheron path samples. In the example notebook (https://github.com/meta-pytorch/botorch/blob/main/tutorials/thompson_sampling/thompson_sampling.ipynb), the maximizer of the matheron path samples is fined via sampling. But as the matheron path samples are fully differentiable determinisitic models, one should be also able to find their maximizers via optimize_acqf. As optimize_acqf expects an acquisition function object, which is the most lightweight acqf that you would recommend for this? In the end we just want to apply an objective (for disctinction between maximization/minimization etc). to the path samples and then want to directly optimize on the path sample/deterministic model. I got it running with qSimpleRegret, but I have the feeling that there should be a more lightweight solution for this.

Any ideas?

Best,

Johannes

[hvarfner]

Hi Johannes! Fairly new add, can be found here. This should have all the functionality that you are looking for, but let us know is something is missing or not working as intended!

[hvarfner]

@TobyBoyne It's just me not being sufficiently precise in the docstring. This refers to the sum over q, so the acquisition value being returned is the summed values over q unique Thompson samples. Description here: https://github.com/meta-pytorch/botorch/blob/main/botorch/acquisition/thompson_sampling.py#L115

[TobyBoyne]

Ah I see, thanks for the clarification!

[hvarfner]

@jduerholt NP!

Yes, the expensive part is the inverse of K(X_train, X_train), but you really must have a lot of data for that to be the practical bottleneck, rather than optimize_acqf?

With that said, I think caching is doable but not very straightforward. You could imagine writing a cached version of gaussian_update (this method). I am not sure how it would make its way to the acqf, but I'd be happy to discuss this further.

[jduerholt]

Thanks, for the info, for my first prototyping of the algorithm, I will go with the current no-cache version, and if necessary, I will have a look into implementing caching into gaussian_update. I will keep you posted!

[Balandat]

One thing to keep in mind is that the summing is really because of the limitation of the optimization implementation, see this comment:

  # NOTE: The current implementation sums over the q-batch dimension, which means
  # that we are optimizing the sum of independent Thompson samples. In the future,
  # we can leverage *batched* L-BFGS optimization, rather than summing over the q
  # dimension, which will guarantee descent steps for all members of the batch
  # through batch-member-specific learning rate selection.

Let me see if there is a gap or whether we can implement this now.