r/MachineLearning - [D] Why is L2 preferred over L1 Regularization?

By assuming our data is distributed roughly as a Gaussian, we can perform a lot of powerful analysis which helps us come up with better, more efficient algorithms which exploit mathematical properties related to Gaussian distributions. More practically speaking, Euclidean distance is the L2 norm, they are the same thing. Rotational invariance is a byproduct of using vector spaces with the L2 norm. And it penalizes large errors much more heavily than small errors, so once your optimization is done it's safe to assume that all the errors are roughly of the same order of magnitude (and distributed roughly like a Gaussian).