How to use LinearTruncatedFidelityKernel in Multi-Fidelity optimization

[samuelkim16]

I am doing multi-fidelity optimization using the SingleTaskMultiFidelityGP with default options. Reading through the documentation of LinearTruncatedFidelityKernel, I have a few questions:

• Because of the deterministic part of the kernel, does that mean the actual values of the fidelity parameter matter for degree of correlation? I.e. fidelities of 0 and 1 will be uncorrelated in the kernel, or if I suspect that my simulations are highly correlated, then setting them close to each other e.g. 0.9 and 1 will tell the kernel to incorporate a high degree of correlation.
• If I suspect that my 2 fidelities have a highly linear correlation (i.e. y2=m*y1+b), is there a way to constrain the kernel to be linear?
• Is there a reference where I can read more about this kernel?

[Balandat]

Because of the deterministic part of the kernel, does that mean the actual values of the fidelity parameter matter for degree of correlation? I.e. fidelities of 0 and 1 will be uncorrelated in the kernel, or if I suspect that my simulations are highly correlated, then setting them close to each other e.g. 0.9 and 1 will tell the kernel to incorporate a high degree of correlation.

Yes, that is the inductive bias of the kernel (though it's been a while since I've thought through this in great detail).

If I suspect that my 2 fidelities have a highly linear correlation (i.e. y2=m*y1+b), is there a way to constrain the kernel to be linear?

Not directly, but it shouldn't be hard to implement a modified kernel that encodes this knowledge.

Is there a reference where I can read more about this kernel?

I don't think this exact kernel has a reference, but it is a variant of the multi-fidelity kernels discussed in Section 5.3 of https://arxiv.org/pdf/1903.04703