I mainly use k-fold cross-validation for parameter tuning and model selection for prediction problems. Now, is there a standard or if not a less-known way to measure the sensitivity of the parameters over the cross-validation error, and to quantify it? Also, is it standard to look at the variability of the cross-validated error across folds as well? I know that the question around the variability has a lot of caveats, but what is a good way to do this, say if I was reporting cross-validation results and the cv errors were either close by/ were relatively changing based on the size of the scaled dataset- then how can I report the variability apart from the cv errors itself?
Note: Assume that I have just two parameters to tune, and I use a discrete grid of the two parameter combinations