Question: is minimizing test set mean validation error more important than the gap between train and test errors?
Let's say I can tweak parameters in my model to give me mean validation error of 4500 RMSE on k-fold cross validation. When I use these parameters I found to compute RMSE on train and test, I get 1500 and 4500, respectively - quite overfit.
Is that still more preferable than a model that would get me, say, 5000 train error, and 5500 test error? Something that performs worse on the test set, but is less overfit to the training set?