okay so why add this regularizer I can already get the global min of the logistic loss without this regularization term what am I getting here is my stat sample complexity much better and it turns out it is let's look at a very simple data set on the first two coordinates the data looks like this it's like two eggs or essentially then every other coordinate is just standard normal so there's two coordinates that have signal and that's the ones you want to pay attention to the rest of the coordinates are completely uncorrelated