If we're going to talk loss functions, then 1-0 loss is most appropriate here. As you say, "Hellp" is really no more or less fit than "Helln" whereas even absol

If we're going to talk loss functions, then 1-0 loss is most appropriate here. As you say, "Hellp" is really no more or less fit than "Helln" whereas even absolute distance wouldn't reflect that. Squaring admits a function into the class of loss functions which must be strictly non-negative to be meaningful, but really it's just always been done to make derivatives easy. If you don't need derivatives (or expectations), you can probably get away without using squared loss if you don't want it.