Factor of 2 in objective for DP logistic regression

[fl16180]

Hi, I wanted to check about a factor of 2 in the implementation regarding the conversion \Lambda = 1 / (2 n C) as discussed in a previous PR #10

In Corollary 11 of [CMS18] their regularization term N(f) = 1/2 ||f||^2 so their proof takes into account the 1/2 factor in the objective formulation (that is, J = 1/n sum(loss) + 1/2 \Lambda ||f||^2 ), just like in the sklearn objective which is J= C*sum(loss) + 1/2 w^t w . So if this is the case then the conversion should be \Lambda = 1 / (n C), and \Lambda = alpha / n, which implies in your code 0.5 * alpha would just be alpha
e.g.

differential-privacy-library/diffprivlib/mechanisms/vector.py

Line 139 in e9bbdb7

epsilon_p = self.epsilon - 2 * np.log(1 + self.function_sensitivity * self.data_sensitivity /

Thank you