Changing the surrogate model - impact on gradients' formula

[CPJClare]

Hello Jian Wu,

I am currently exploring the use of different surrogates, as a Gaussian alternative and am considering building upon your gradients' work in Cornell-MOE to do so.

I have been reading your "Bayesian Optimization with Gradients" paper from NIPS 2017 - congratulations on an excellent paper. In Equation 3.3, you list the multi-output formula in terms of the Gaussian mean and covariance functions.

Assume the probabilistic model then changes, from say, Gaussian Processes (GPs), to multivariate Student-t, with a different mean and covariance function for the underlying Student-t process (STP).

Would Equation 3.3 remain the same (but with different STP mean and covariance inputs)?

OR

Does Equation 3.3 have to change, each time the underlying surrogate model changes, to reflect the properties of the new probabilistic model? For example, how would going from GPs to Random Forests work?

I would obviously then look to program any amendments into my own code, using Cornell-MOE as my starting-point (with citation).

Thank you.

Regards,
Conor Clare