  We propose a novel framework for the differentially private ERM, input
perturbation. Existing differentially private ERM implicitly assumed that the
data contributors submit their private data to a database expecting that the
database invokes a differentially private mechanism for publication of the
learned model. In input perturbation, each data contributor independently
randomizes her/his data by itself and submits the perturbed data to the
database. We show that the input perturbation framework theoretically
guarantees that the model learned with the randomized data eventually satisfies
differential privacy with the prescribed privacy parameters. At the same time,
input perturbation guarantees that local differential privacy is guaranteed to
the server. We also show that the excess risk bound of the model learned with
input perturbation is $O(1/n)$ under a certain condition, where $n$ is the
sample size. This is the same as the excess risk bound of the state-of-the-art.
