We consider data release protocols for data $X=(S,U)$, where $S$ is sensitive; the released data $Y$ contains as much information about $X$ as possible, measured as $\operatorname{I}(X;Y)$, without leaking too much about $S$. We introduce the Robust Local Differential Privacy (RLDP) framework to measure privacy. This framework relies on the underlying distribution of the data, which needs to be estimated from available data. Robust privacy guarantees are ensuring privacy for all distributions in a given set $\mathcal{F}$, for which we study two cases: when $\mathcal{F}$ is the set of all distributions, and when $\mathcal{F}$ is a confidence set arising from a $\chi^2$ test on a publicly available dataset. In the former case we introduce a new release protocol which we prove to be optimal in the low privacy regime. In the latter case we present four algorithms that construct RLDP protocols from a given dataset. One of these approximates $\mathcal{F}$ by a polytope and uses results from robust optimisation to yield high utility release protocols. However, this algorithm relies on vertex enumeration and becomes computationally inaccessible for large input spaces. The other three algorithms are low-complexity and build on randomised response. Experiments verify that all four algorithms offer significantly improved utility over regular LDP.

中文翻译：

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鲁棒的本地差异隐私的隐私-实用性权衡

我们考虑数据$ X =（S，U）$的数据发布协议，其中$ S $是敏感的；释放的数据$ Y $包含尽可能多的有关$ X $的信息（以$ \ operatorname {I}（X; Y）$度量），而不会泄漏太多有关$ S $的信息。我们引入了稳健的本地差分隐私（RLDP）框架来衡量隐私。该框架依赖于数据的基础分布，需要根据可用数据进行估算。健壮的隐私保证可确保给定集合$ \ mathcal {F} $中所有分布的隐私，为此我们研究两种情况：$$ mathcal {F} $是所有分布的集合，以及$ \ mathcal {F } $是对公开数据集进行$ \ chi ^ 2 $测试产生的置信度集。在前一种情况下，我们引入了一个新的发布协议，该协议被证明在低隐私权制度下是最佳的。在后一种情况下，我们提出了四种从给定数据集中构造RLDP协议的算法。其中的一个近似为多面体$ \ mathcal {F} $，并使用强大的优化结果来生成高实用性的发布协议。但是，该算法依赖于顶点枚举，并且对于大输入空间在计算上变得不可访问。其他三种算法是低复杂度的，并且建立在随机响应上。实验证明，与常规LDP相比，所有四种算法均提供了显着改善的实用性。其他三种算法是低复杂度的，并且建立在随机响应上。实验证明，与常规LDP相比，所有四种算法均提供了显着改善的实用性。其他三种算法是低复杂度的，并且建立在随机响应上。实验证明，与常规LDP相比，所有四种算法均提供了显着改善的实用性。