Differentially Private Generalized Linear Models Revisited

Understand

We study the problem of $(\epsilon,\delta)$-differentially private learning of linear predictors with convex losses.

• We provide results for two subclasses of loss functions.
• The first case is when the loss is smooth and non-negative but not necessarily Lipschitz (such as the squared loss).
• For this case, we establish an upper bound on the excess population risk of $\tilde{O}\left(\frac{\Vert w^*\Vert}{\sqrt{n}} + \min\left\{\frac{\Vert w^* \Vert^2}{(n\epsilon)^{2/3}},\frac{\sqrt{d}\Vert w^*\Vert^2}{n\epsilon}\right\}\right)$, where $n$ is the number of samples, $d$ is the dimension of the problem, and $w^*$ is the minimizer of the population risk.