Optimality of Matrix Mechanism on $\ell_p^p$-metric
<|reference_start|>Optimality of Matrix Mechanism on $\ell_p^p$-metric: In this paper, we introduce the $\ell_p^p$-error metric (for $p \geq 2$) when answering linear queries under the constraint of differential privacy. We characterize such an error under $(\epsilon,\delta)$-differential privacy. Before this paper, tight characterization in the hardness of privately answering linear queries was known under $\ell_2^2$-error metric (Edmonds et al., STOC 2020) and $\ell_p^2$-error metric for unbiased mechanisms (Nikolov and Tang, ITCS 2024). As a direct consequence of our results, we give tight bounds on answering prefix sum and parity queries under differential privacy for all constant $p$ in terms of the $\ell_p^p$ error, generalizing the bounds in Henzinger et al. (SODA 2023) for $p=2$.<|reference_end|>
@article{liu2024optimality,
    title={Optimality of Matrix Mechanism on $\ell_p^p$-metric},
    author={Jingcheng Liu and Jalaj Upadhyay and Zongrui Zou},
    journal={arXiv preprint arXiv:2406.02140},
    year={2024},
    archivePrefix={arXiv},
    eprint={2406.02140},
    primaryClass={cs.CR cs.LG}
}