Empirical Risk Minimization in Non-interactive Local Differential Privacy Revisited

In this paper, we revisit the Empirical Risk Minimization problem in the noninteractive local model of differential privacy. In the case of constant or low dimensions (p n), we first show that if the loss function is (, T)-smooth, we can avoid a dependence of the sample complexity, to achieve error α, on the exponential of the dimensionality p with base 1/α (i.e., α