I understand that you are curious to know about "KernelScales" optimization for ARD kernels.
In Gaussian Process Regression (GPR) models, especially when using Automatic Relevance Determination (ARD) kernels, the "KernelScale" parameters are crucial as they determine the length scales for each dimension of the input data. When you use the "fitrgp" function in MATLAB, the initial "KernelParameters" you specify can indeed change during the fitting process. This is because "fitrgp" typically optimizes these parameters to best fit the training data.
You are indeed corect in you understanding that, "KernelScale" cannot be optimized for any of the ARD kernels. This has been specified in the following part of the documentation KernelScale Optimization
The documentation does not explicitly mention how the value is determined. However, it does provide information about the search range over which the parameter is varied for achieving an optimal fit. Please find below an extract from Release Notes of R2023b concerning search range of "KernelScale" hyperparameter.
Starting from MATLAB R2023b, "KernelScale" hyperparameter search range does not depend upon predictor data during optimization of GPR models i.e. when you specify to optimize the GPR hyperparameter "KernelScale" by leveraging the "OptimizeHyperparameters" name-value argument, it searches among positive values log-scaled in the range 
instead of 
where 
.
instead of where .I hope ths helps.
