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[Feature Request] MultiTaskGP with multiple task features #2359

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@AdrianSosic

Description

@AdrianSosic

🚀 Feature Request

Currently, the MultiTaskGP expects exactly one task dimension, specified via the task_feature argument. It would be great to extend the model such that it can handle several task dimensions.

Pitch

Describe the solution you'd like
I see no reason why the internal logic could not be straightforwardly generalized to handle multiple task dimensions, since the corresponding feature enters multiplicatively via an IndexKernel. That means, additional task dimensions could be treated in the exact same way, as additional factors to the kernel product.

Describe alternatives you've considered
Allowing to specify multiple task dimensions would enable learning models over structured tasks spaces – as opposed to the alternative where several such dimensions would be flattened into a single one before entering the MultiTaskGP.

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