BUG: MBM sums up MOO outputs when given a single objective acquisition function about ax

[saitcakmak]

So, the part about constructing a multi-output surrogate model is correct. That should indeed happen. The issue is scalarizing the outputs from the model, using an arbitrary sum. We do support ScalarizedObjective, which is the intentional way of doing this, where the user can specify the scalarization weights.

qNParEGO is also different here, since it is a multi-objective acquisition function that internally uses a scalarization. It is defined to work with multiple objectives and the behavior is by design.

The issue is doing this silently using arbitrary weights (well, they're just 1 for maximization and -1 for minimization) with acquisition functions that are not designed for multi-objective optimization.

[Abrikosoff]

Actually, in my (very limited) knowledge, isn't this how MOBO is supposed to work? If you look at the BoTorch documentation for MOBO, especially where the model is initialized, you find:

def initialize_model(train_x, train_obj):
    # define models for objective and constraint
    train_x = normalize(train_x, problem.bounds)
    models = []
    for i in range(train_obj.shape[-1]):
        train_y = train_obj[..., i : i + 1]
        train_yvar = torch.full_like(train_y, NOISE_SE[i] ** 2)
        models.append(
            FixedNoiseGP(
                train_x, train_y, train_yvar, outcome_transform=Standardize(m=1)
            )
        )
    model = ModelListGP(*models)
    mll = SumMarginalLogLikelihood(model.likelihood, model)
    return mll, model

(in our case we are discussing SingleTaskGPs, but this does not change the nature of the problem, I think). If this tracks I would think that a ModelList containing two SingleTaskGPs would be the way to do MOBO as well, no?

Edit: This is the case for qNParEGO at least, for example, which uses Chebyshev scalarization, as far as I can see.