规避加性误差障碍的私有翻转流持续发布
Skirting Additive Error Barriers for Private Turnstile Streams
AI总结：
本文提出在私有翻转流中持续发布不同元素数量的方法，通过结合乘性和加性误差降低空间需求，同时探讨隐私与误差间的权衡。
摘要：
我们研究了在翻转流中实现差分隐私的连续发布不同项目数量的问题，其中项目可能被插入和删除。最近的一项工作（NeurIPS '23）表明，对于长度为T的流，即使没有空间限制，也需要多项式加性误差Ω(T^{1/4})。我们证明，如果允许算法输出具有加性与乘性误差的估计值，则可以绕过这一加性误差下界。我们给出了一个算法，用于在翻转流中持续发布不同元素数量，具有多项式对数T的乘性和多项式对数T的加性误差。我们还展示了在估计翻转流的F2矩时，存在类似现象，其中可以得到1+o(1)的乘性和多项式对数T的加性误差。这两个结果可以在多项式对数空间内实现，而先前的方法使用的是多项式空间。在亚线性空间范围内，即使不考虑隐私，某些乘性误差也是必要的。我们提出了几个开放性问题，旨在更好地理解隐私持续发布中乘性误差和加性误差之间的权衡。
英文摘要：
We study differentially private continual release of the number of distinct items in a turnstile stream, where items may be both inserted and deleted. A recent work of Jain, Kalemaj, Raskhodnikova, Sivakumar, and Smith (NeurIPS '23) shows that for streams of length $T$, polynomial additive error of $Ω(T^{1/4})$ is necessary, even without any space restrictions. We show that this additive error lower bound can be circumvented if the algorithm is allowed to output estimates with both additive \emph{and multiplicative} error. We give an algorithm for the continual release of the number of distinct elements with $\text{polylog} (T)$ multiplicative and $\text{polylog}(T)$ additive error. We also show a qualitatively similar phenomenon for estimating the $F_2$ moment of a turnstile stream, where we can obtain $1+o(1)$ multiplicative and $\text{polylog} (T)$ additive error. Both results can be achieved using polylogarithmic space whereas prior approaches use polynomial space. In the sublinear space regime, some multiplicative error is necessary even if privacy is not a consideration. We raise several open questions aimed at better understanding trade-offs between multiplicative and additive error in private continual release.
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。
