矩阵机制在 $\ell_p^p$-度量上的最优性
Optimality of Matrix Mechanism on $\ell_p^p$-metric
AI总结：
本文在差分隐私下引入 $\ell_p^p$-误差度量，刻画了 $(ε,δ)$-差分隐私下回答线性查询的误差紧致界限，推广了前缀和与奇偶校验查询在 $p=2$ 时的已知结果。
摘要：
本文在差分隐私约束下回答线性查询时，引入了 $\ell_p^p$-误差度量（适用于 $p \geq 2$）。我们在 $(ε,δ)$-差分隐私下刻画了此类误差。在本文之前，已知在 $\ell_2^2$-误差度量（Edmonds 等人，STOC 2020）和无偏机制的 $\ell_p^2$-误差度量（Nikolov 和 Tang，ITCS 2024）下，隐私回答线性查询难度的紧致刻画。作为结果的直接推论，我们给出了在差分隐私下，以 $\ell_p^p$ 误差衡量时回答前缀和与奇偶校验查询的紧致界限（对所有常数 $p$），推广了 Henzinger 等人（SODA 2023）针对 $p=2$ 的界限。
英文摘要：
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 $(ε,δ)$-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 $p=2$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
