Add Multi Information Source Augmented GP

[andreaponti5]

Motivation

This pull request introduces the implementation of the Augmented Gaussian Process (AGP) and a related acquisition function based on UCB, namely Augmented UCB (AUCB), for multi information source problems.

Candelieri, A., Archetti, F. Sparsifying to optimize over multiple information sources: an augmented Gaussian process based algorithm. Struct Multidisc Optim 64, 239–255 (2021). https://doi.org/10.1007/s00158-021-02882-7

AGP and AUCB in a nutshell

The key idea of the AGP is to fit a GP model for each information source and augment the observations on the high fidelity source with those from cheaper sources which can be considered as reliable. The GP model fitted on this augmented set of observations is the AGP.

The AUCB is a modification of the standard UCB - computed on the AGP - suitably proposed to also deal with the source-specific query cost.

Example

This is what the AGP and AUCB look like on the Forrester problem considering 2 sources.

Some implementation details

The Augmented GP implementation is based on the SingleTaskGP.
Each source is implemented as an independent SingleTaskGP and all the reliable observations are used to fit the SingleTaskGP representing the AGP, namely SingleTaskAugmentedGP. A key difference with the Multi-Fidelity approaches in BoTorch, is that the dimension representing the source is not directly modelled by the AGP.
In addition, a Fixed-Noise version of the AGP has been implemented based on the FixedNoiseGP.

The Augmented UCB implementation is based on the UpperConfidenceBound, but it is penalized by the cost of the source and the discrepancy from the AGP.

Have you read the Contributing Guidelines on pull requests?

Yes, I have read the Contributing Guidelines on pull requests.

Test Plan

A bunch of unit tests for both, the AGP and AUCB, has been implemented. Those are inspired by the SingleTaskGP and UpperConfidenceBound tests, respectively.

In addition, a notebook tutorial shows how to use the AGP model along with the AUCB acquisition function and a comparison with the Multi-Fidelity MES on the Augmented Branin test function.

Finally, we plan to release an arXiv soon, with an extensive comparison of Multi-Fidelity and Multi Information Source approaches in BoTorch. Here are some preliminary results on the Augmented Hartmann test function, considering three sources (with fidelities $[0.50, 0.75, 1.00]$). The AGP has been compared with the discrete Multi-Fidelity version of the Knowled Gradient (KG), Max-value Entropy Search (MES) and GIBBON. The figure on the left shows the best seen with respect to the query cost, while the figure on the right shows the best seen with respect to the wall-clock time.

Related PRs

The docs has been updated in this PR.

[sdaulton]

Thanks for putting up the PR! This works looks quite interesting!

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[saitcakmak]

Hi @andreaponti5. Thanks for the PR! We're trying out a new support model for community contributions: https://github.com/pytorch/botorch/blob/main/CONTRIBUTING.md#community-contributions-beta. Can you move the new additions to the botorch_community, notebooks_community & test_community directories and add the contributor info and other metadata to the files as outlined in the readme files? Thanks!

[Balandat]

Thanks - looks like there are some minor lint and auto-sort code formatting issues. I also left a couple of inline comments that would be great to address (though potentially ok to do this in a follow-up PR).

[Balandat]

what happened here?

[andreaponti5]

Not sure what happened. I removed SingleTaskAugmentedGP from the doc. Community contributions shouldn't go in the documentation, right?

[Balandat]

@saitcakmak what are your thoughts re community contribs? Would be nice if we generated docs as part of the community modules (maybe not part of the core modules) given that people are putting effort into their docstrings (thanks!).

[saitcakmak]

Yeah, I think it'd be good to have generated docs for community modules on the website. We can build it when building the community tutorials for the website.

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@sdaulton has imported this pull request. If you are a Meta employee, you can view this diff on Phabricator.

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@sdaulton merged this pull request in defe657.

[Balandat]

Merged! Thanks again @andreaponti5 for your contribution.