Faster Learning under Relaxed Local Differential Privacy

Under a relaxed local differential privacy formulation bounded by total variation distance (α-TV-LDP), this paper re-evaluates density estimation rates. By perturbing sensitive observations with symmetrized Gamma noise, the authors establish that deconvolution estimators over r-Sobolev spaces attain a pointwise convergence rate of (nα)^{-(2r-1)/(2r)}, narrowing the statistical gap toward the non-private minimax baseline. Applied to neural network estimation, the framework circumvents the iterative gradient corruption typical of DP-SGD, improving empirical estimation efficiency over standard Laplace mechanisms.