Just to verify, it wouldn’t make sense for the training set and validation set to have different loss functions right? Because then they would be held accountable differently.
Yes you are correct it wouldn’t make any sense to have differnet loss functions for training set and validation set.
Well, in theory it could be 2 different loss functions if the scores would participate in some sort of forum competition.
You could train with whatever loss function you want, as long as the test set is being evaluated with the same loss function for everyone.
You of course loose the ability to compare the results on a single graph.