差分隐私遇上固定参数可解性：算法与下界

中文摘要 AI 辅助

我们研究了在ε-差分隐私（ε-DP）约束下的组合优化问题。鉴于显式输出解存在强下界，我们在Gupta等人（SODA 2010）的隐式表示框架内工作，其中私有的多项式时间随机化“编码器”生成解的表示，而“解码器”利用该表示及输入来提取有效的最终解。在本工作中，我们通过允许编码器以固定参数可解时间运行来推广此框架。这规避了多项式时间算法固有的近似障碍，并为许多基础组合优化问题获得了改进的保证。最后，我们为我们的框架建立了首个与表示无关的下界。假设Gap指数时间假设的非均匀变体成立，对于足够小的ε>0，我们证明如果解码器以亚指数时间运行，则不存在ε-DP编码器-解码器对能够达到某些近似保证。我们进一步提供了即使对于更大的ε也成立的与表示相关的下界。

英文摘要

We study combinatorial optimization problems under the constraint of $ε$-differential privacy ($ε$-DP). Given the strong lower bounds for explicitly outputting solutions, we work within the implicit representation framework of Gupta et al. (SODA 2010), where a private polynomial-time randomized "encoder" generates a representation of a solution, and a "decoder" uses this representation along with the input to extract a valid final solution. In this work, we generalize this framework by allowing the encoder to run in fixed-parameter tractable time. This circumvents approximation barriers inherent to polynomial-time algorithms and obtains improved guarantees for many fundamental combinatorial optimization problems. Finally, we establish the first representation-independent lower bounds for our framework. Assuming a non-uniform variant of the Gap Exponential Time Hypothesis, for sufficiently small $ε> 0$, we prove that no $ε$-DP encoder-decoder pair can achieve certain approximation guarantees, if the decoder runs in subexponential time. We further provide representation-dependent lower bounds that hold even for larger $ε$.

发表机构

• Google Research（谷歌研究院）

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