随机响应机制效用优化研究

Study on utility optimization for randomized response mechanism

针对本地化差分隐私中的隐私-效用均衡问题,对差分隐私和近似差分隐私情形下的二元广义随机响应机制建立效用优化模型,并采用图解法、最优性证明、软件求解和极值点等方法求解,得到了效用最优值与隐私预算、输入数据分布的精确表达式,给出了相应的效用最优机制。研究结果表明效用最优值和效用最优机制均与隐私预算和输入数据分布相关。另外,多元随机响应机制效用优化模型可通过本地化差分隐私极值点来求解。

For the study of privacy-utility trade-off in local differential privacy,the utility optimization models of binary generalized random response mechanism for the case of differential privacy and approximate differential privacy were established.By graphic method,optimality proof,software solution and extreme point method,the exact expression of the optimal utility with privacy budget and the distribution of input data was obtained,and the corresponding optimal randomized response mechanism was given.The results show that both the optimal utility and optimal mechanism are related to privacy budget and input data distribution.Moreover,the discussion for multivariate randomized response mechanism shows that the method of extreme points of local differential privacy is feasible to the solution.