Study on utility optimization for randomized response mechanism

Abstract

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.

Keywords

• local differential privacy;randomized response;utility optimization;extreme point;simplex method