Approximate Differential Privacy of the $\ell_2$ Mechanism

We study the $\ell_2$ mechanism for computing a $d$-dimensional statistic with bounded $\ell_2$ sensitivity under approximate differential privacy. Across a range of privacy parameters, we find that the $\ell_2$ mechanism obtains lower error than the Laplace and Gaussian mechanisms, matching the former at $d=1$ and approaching the latter as $d \to \infty$.

@article{joseph2025_2502.15929,
  title={ Approximate Differential Privacy of the $\ell_2$ Mechanism },
  author={ Matthew Joseph and Alex Kulesza and Alexander Yu },
  journal={arXiv preprint arXiv:2502.15929},
  year={ 2025 }
}