Low fidelity model in Multi-fidelity bayesian optimization and machine learning model at LF

[Kh-im]

Hello everyone,

I'm working on multi-objective, multi-fidelity methods, and I have some questions about the use of low-fidelity simulation, particularly when the low-fidelity simulation is derived from a machine learning model:

1. Suppose we have n high-fidelity points from past experiments. The cost of the low-fidelity model is almost zero. How does this influence the choice of the next high-fidelity point? Do we run low-fidelity simulations until the low-fidelity EI is evaluated "everywhere"?

2. The low-fidelity model can be a machine learning model or an analytical model that approximates the objective over a larger search space of the problem we want to solve. Our problem is in a part of the space that has not been well explored. What is the best modeling strategy: simply consider this model as a low-fidelity simulation and add the high-fidelity points generated for training to this model, or use a single-fidelity strategy but replace the Gaussian model with this model?

Thanks for your help and for this incredible code, BoTorch.

[esantorella]

The cost of the low-fidelity model is almost zero. How does this influence the choice of the next high-fidelity point? Do we run low-fidelity simulations until the low-fidelity EI is evaluated "everywhere"?

It depends what acquisition function you use. If you use multi-fidelity hypervolume knowledge gradient as described in the MF-HVKG tutorial, lowering the cost of the low-fidelity model will lead to evaluating more low-fidelity points. If you already have some high-fidelity points, I do expect that in the limit as the cost of the low-fidelity points falls towards zero, you would evaluate almost entirely low-fidelity points, but it's hard to say how this would play out in a realistic setting.

As for your second question, I think following the MF-HVKG tutorial would be reasonable in this situation. It would probably lead to generating a mix of low-fidelity and high-fidelity points. But I am not an expert on this kind of setup.

[Balandat]

The other thing to keep in mind is that if the low fidelity evaluation is truly "more or less free", then a classic (e.g. MF-HVKG) multi-fidelity method may not be the best approach since it will suffer from scalability challenges with man y low-fidelity observations. Instead, one could consider other approaches, such as using a model fit on a lot of low-fidelity data as the prior mean for the surrogate model.

[Kh-im]

Thanks, I think that my subject is similar to #2758. I have a lot of time between each HF (days) so scalability may not be a problem.

@Balandat, how can I fit on low-fidelity data as the prior mean before beginning the optimization in BoTorch ?

Thanks for your help