multi objective Bayesian optimization

[lovecodng]

Does this package supports multi objective Bayesian optimization (MOBO)? If so is there a documentary or examples that can be used to understand how MOBO is applied using this pakckage?

[saitcakmak]

This tutorial may be helpful: https://botorch.org/tutorials/multi_objective_bo

In addition, Ax, which uses BoTorch under the hood, may also be interesting: https://ax.dev/tutorials/multiobjective_optimization.html. You may prefer to use Ax if you're interested in optimizing some objective without dealing with all the details, and BoTorch if you're doing BO research / developing your own methods / need lots of customization etc.

[saitcakmak]

I see that you're defining model_qparego2 but later using model_2. That may be leading to some errors. Otherwise, this looks like a correct use of ModelListGP.

[A-ep93]

There are two tutorials for multi-objective MO on the website. Here are the links: Link1, link2
Why there is not use of ModelListGP in those tutorials?

[saitcakmak]

I can't really think of any particular reason other than that using a SingleTaskGP leads to fewer lines of code and keeps the tutorial simple. If you want to use ModelListGP, you can replace the initialize_model method of those notebooks with the following:

def initialize_model(train_x, train_obj):
    models = [
        SingleTaskGP(
            train_x,
            train_obj[..., i : i + 1],
            outcome_transform=Standardize(m=1),
        )
        for i in range(train_obj.shape[-1])
    ]
    model = ModelListGP(*models)
    mll = SumMarginalLogLikelihood(model.likelihood, model)
    return mll, model

[A-ep93]

Thanks for your response @saitcakmak. In the previous replies of this post, it has been mentioned that similar to a single output, for multi-output also, we need to use ExactMarginalLogLikelihood. However, in the code you sent, you used SumMarginalLogLikelihood. Can you please let me know the reason for this?

[Balandat]

I can't really think of any particular reason other than that using a SingleTaskGP leads to fewer lines of code and keeps the tutorial simple

One other reason for using SingleTaskGP is that since it uses pytorch batch evaluation under the hood (rather than sequential evaluation of two models) it is usually faster to do predictions and thus optimize the acquisition function.