I got a more theoretical question here: I have done some research about the L2 (Ridge) and L1 (Lasso) regularizations. I know the formula, and understand the aim of those two different procedures. The crucial difference between the two approaches is that L1 takes the absolute value while L2 takes the squared value of coefficients multiplied by the hyperparameter lambda. However, it is still not clear to me why L2 regularization cannot shrink parameters down to zero and L1 can. I can't see this from the formula. Could someone please explain this to me (probably with one example).
L1 Regularization:
L2 Regularization:
Thanks for your help!