  Traditionally, there are two models on differential privacy: the central
model and the local model. The central model focuses on the machine learning
model and the local model focuses on the training data. In this paper, we study
the \textit{input perturbation} method in differentially private empirical risk
minimization (DP-ERM), preserving privacy of the central model. By adding noise
to the original training data and training with the `perturbed data', we
achieve ($\epsilon$,$\delta$)-differential privacy on the final model, along
with some kind of privacy on the original data. We observe that there is an
interesting connection between the local model and the central model: the
perturbation on the original data causes the perturbation on the gradient, and
finally the model parameters. This observation means that our method builds a
bridge between local and central model, protecting the data, the gradient and
the model simultaneously, which is more superior than previous central methods.
Detailed theoretical analysis and experiments show that our method achieves
almost the same (or even better) performance as some of the best previous
central methods with more protections on privacy, which is an attractive
result. Moreover, we extend our method to a more general case: the loss
function satisfies the Polyak-Lojasiewicz condition, which is more general than
strong convexity, the constraint on the loss function in most previous work.
