An algorithm is developed to gradually relax the Differential Privacy (DP) guarantee of a randomized response. The output from each relaxation maintains the same probability distribution as a standard randomized response with the equivalent DP guarantee, ensuring identical utility as the standard approach. The entire relaxation process is proven to have the same DP guarantee as the most recent relaxed guarantee. The DP relaxation algorithm is adaptable to any Local Differential Privacy (LDP) mechanisms relying on randomized response. It has been seamlessly integrated into RAPPOR, an LDP crowdsourcing string-collecting tool, to optimize the utility of estimating the frequency of collected data. Additionally, it facilitates the relaxation of the DP guarantee for mean estimation based on randomized response. Finally, numerical experiments have been conducted to validate the utility and DP guarantee of the algorithm.

翻译：本文提出了一种逐步放宽随机响应差分隐私（DP）保证的算法。每次放宽后的输出与具有等效DP保证的标准随机响应保持相同的概率分布，从而确保其效用与标准方法一致。整个放宽过程被证明具有与最临近放宽保证相同的DP保证。该DP放宽算法可适配于任何依赖于随机响应的局部差分隐私（LDP）机制。该算法已无缝集成至RAPPOR（一种基于LDP的众包字符串收集工具）中，以优化收集数据频率估计的效用。此外，该算法还可促进基于随机响应的均值估计中DP保证的放宽。最后，通过数值实验验证了该算法的效用与DP保证。