Say my training loss is 0.5 and my validation loss is 2.5 (both have stopped decreasing, validation loss never increased). I am clearly overfitting. If I add regularization, my training loss becomes 1 and validation loss 3.5.
The first model clearly has better validation loss, and the second model overfits less.
Which model should be selected? Is it even possible that a model that overfits more performs better on unseen data or does this mean that there is data leakage of some sort?
The problem here is that I'm not doing simple things like image classification but trying something more complicated and I'm not finding a lot of resources on overfitting on problems that have not yet been solved. Mostly it's disussions of binary image classification where it's possible to find models that get a very good validation error, so the explanations don't apply to my problems.