arXivDaily arXiv每日学术速递 周一至周五更新
arXiv周末暂无论文更新,休息一下吧,周末愉快~~
arXiv 2602.06756cs.CR
收藏

$f$-差分隐私过滤器:有效性与近似解

$f$-Differential Privacy Filters: Validity and Approximate Solutions

University of Helsinki(赫尔辛基大学);Nokia Bell Labs(诺基亚贝尔实验室);CISPA Helmholtz Center for Information Security(CISPA 亥姆霍兹信息安全中心)

Long Tran, Antti Koskela, Ossi Räisä, Antti Honkela

AI总结:

本文研究了在完全自适应组合下,$f$-差分隐私过滤器的有效性问题,提出近似解并证明了其在渐近情况下优于RDP方法。

摘要:

在差分隐私中,考虑完全自适应组合下的隐私损失是一个核心挑战。隐私过滤器是确保全球预算不被超支的停止规则。$f$-DP是优化过滤器设计的领先候选者,它通过分段线性折中函数恢复$(\varepsilon,δ)$-DP,同时在标准组合中通过张量积实现紧密的$(\varepsilon,δ)$-DP会计。然而,是否能够在$f$-DP下正确定义此类过滤器仍不清楚。本文证明了自然$f$-DP过滤器——跟踪路径累积张量积并在指定曲线被穿越时停止——本质上无效,从而排除了在完全自适应设置中直接使用标准高效快速傅里叶变换会计的可能。我们还证明了$f$-DP的完全自适应中心极限定理,建立了在完全自适应下累积隐私损失的高斯收敛性。作为演示,我们构造了一个闭式近似GDP过滤器,用于子采样高斯机制,证明其在渐近情况下($q\ll 1$和$q\approx 1$)优于RDP方法,无需跟踪完整的折中函数,表明RDP中的松弛并非自适应组合的本质特性——尽管基于CLT的近似在实际子采样率下被认为是乐观的,但这一限制仍是一个开放挑战。

英文摘要:

Accounting for privacy loss under fully adaptive composition -- where mechanism choice and privacy parameters may depend on the history of prior outputs -- is a central challenge in differential privacy (DP). Here, privacy filters are stopping rules ensuring a prescribed global budget is not exceeded. A leading candidate for optimal filter design is $f$-DP, which characterizes the full extent of adversarial hypothesis testing and recovers $(\varepsilon,δ)$-DP through piece-wise linear trade-off functions, while enabling tight $(\varepsilon,δ)$-DP accounting in standard compositions via tensor products. Yet whether such filters can be correctly defined under $f$-DP remains unclear. We show that the natural $f$-DP filter -- tracking path-wise accumulating tensor products and stopping when the prescribed curve is crossed -- is fundamentally invalid, precluding the direct use of standard efficient numerical Fast-Fourier-Transform accounting in the fully adaptive setting. We characterize this failure, establishing necessary and sufficient conditions for the natural filter's validity. Furthermore, we prove a fully adaptive central limit theorem for $f$-DP, establishing Gaussian convergence of cumulative privacy losses under full adaptivity. As a demonstration, we construct a closed-form approximate GDP filter for subsampled Gaussian mechanisms that provably outperforms RDP-based accounting in asymptotic regimes ($q\ll 1$ and $q\approx 1$) without tracking the full trade-off function, demonstrating that the slack in RDP is not intrinsic to adaptive composition -- though CLT-based approximations are known to be optimistic at realistic subsampling rates, a limitation that remains an open challenge.

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。

↑