Bipartite Randomized Response Mechanism for Local Differential Privacy

Abstract: 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 many cases, both data providers and data analysts hope to maximize the utility of released data. In this paper, we study the fundamental trade-off formulated as a constrained optimization problem: maximizing data utility subject to the constraint of LDP budgets. In particular, the Generalized Randomized Response (GRR) treats all discrete data equally except for the true data. For this, we introduce an adaptive LDP mechanism called Bipartite Randomized Response (BRR), which solves the above privacy-utility maximization problem from the global standpoint. We prove that for any utility function and any privacy level, solving the maximization problem is equivalent to confirming how many high-utility data to be treated equally as the true data on release probability, the outcome of which gives the optimal randomized response. Further, solving this linear program can be computationally cheap in theory. Several examples of utility functions defined by distance metrics and applications in decision trees and deep learning are presented. The results of various experiments show that our BRR significantly outperforms the state-of-the-art LDP mechanisms of both continuous and distributed types.