Categorical Kernel

[jduerholt]

I was wondering why the categorical kernel in (https://github.com/pytorch/botorch/blob/main/botorch/models/kernels/categorical.py) is of the form exp(-dist(x1, x2) / lengthscale) instead of exp(-dist(x1, x2)**2 / lengthscale), where the latter would correspond to an RBF kernel just with a different distance metric.

Is there any specific (mathematical) reason for this?

[jduerholt]

This was a stupid question ;) With the used distance metric in this case, which can be either 0 or 1, exp(-dist(x1, x2) / lengthscale) is the same as exp(-dist(x1, x2)**2/ lengthscale).