With the increasing importance of data privacy, Local Differential Privacy (LDP) has recently become a strong measure of privacy for protecting each user's privacy from data analysts without relying on a trusted third party. In this paper, we consider the problem of high-utility differentially private release. Given a domain of finite integers {1,2,...,N} and a distance-defined utility function, our goal is to design a differentially private mechanism that releases an item with the global expected error as small as possible. The most common LDP mechanism for this task is the Generalized Randomized Response (GRR) mechanism that treats all candidates equally except for the true item. In this paper, we introduce Bipartite Randomized Response mechanism (BRR), which adaptively divides all candidates into two parts by utility rankings given priori item. In the local search phase, we confirm how many high-utility candidates to be assigned with high release probability as the true item, which gives the locally optimal bipartite classification of all candidates. For preserving LDP, the global search phase uniformly selects the smallest number of dynamic high-utility candidates obtained locally. In particular, we give explicit formulas on the uniform number of dynamic high-utility candidates. The global expected error of our BRR is always no larger than the GRR, and can offer a decrease with a small and asymptotically exact factor. Extensive experiments demonstrate that BRR outperforms the state-of-the-art methods across the standard metrics and datasets.

翻译：随着数据隐私重要性日益凸显，本地差分隐私（LDP）近期已成为一种强有力的隐私度量标准，它能在不依赖可信第三方的情况下保护每个用户的隐私免受数据分析者侵害。本文研究高效用差分隐私发布问题：给定有限整数域{1,2,...,N}及距离定义的效用函数，我们的目标是设计一种差分隐私机制，使得发布项的全局期望误差尽可能小。该任务最常用的LDP机制是广义随机响应（GRR）机制，该机制对所有候选项（除真实项外）采取同等处理。本文提出二分随机响应机制（BRR），该机制根据先验项给出的效用排序自适应地将所有候选项划分为两个部分。在局部搜索阶段，我们确定将多少个高效用候选项分配与真实项相同的高发布概率，从而得到所有候选项的局部最优二分分类。为保持LDP特性，全局搜索阶段会统一选择局部获得的动态高效用候选项的最小数量。特别地，我们给出了动态高效用候选项统一数量的显式计算公式。BRR的全局期望误差始终不大于GRR，且能以微小且渐近精确的系数实现误差降低。大量实验表明，BRR在标准评估指标和数据集上均优于现有最优方法。