Interpolation-Based Optimization for Enforcing lp-Norm Metric Differential Privacy in Continuous and Fine-Grained Domains
This work addresses privacy protection in continuous data settings like location tracking, representing an incremental improvement over existing methods.
The paper tackles the challenge of optimizing metric differential privacy in fine-grained or continuous domains by proposing an interpolation-based framework that uses sparse anchor points and log-convex combinations, with experiments on location datasets showing it offers rigorous privacy and competitive utility while outperforming baselines.
Metric Differential Privacy (mDP) generalizes Local Differential Privacy (LDP) by adapting privacy guarantees based on pairwise distances, enabling context-aware protection and improved utility. While existing optimization-based methods reduce utility loss effectively in coarse-grained domains, optimizing mDP in fine-grained or continuous settings remains challenging due to the computational cost of constructing dense perterubation matrices and satisfying pointwise constraints. In this paper, we propose an interpolation-based framework for optimizing lp-norm mDP in such domains. Our approach optimizes perturbation distributions at a sparse set of anchor points and interpolates distributions at non-anchor locations via log-convex combinations, which provably preserve mDP. To address privacy violations caused by naive interpolation in high-dimensional spaces, we decompose the interpolation process into a sequence of one-dimensional steps and derive a corrected formulation that enforces lp-norm mDP by design. We further explore joint optimization over perturbation distributions and privacy budget allocation across dimensions. Experiments on real-world location datasets demonstrate that our method offers rigorous privacy guarantees and competitive utility in fine-grained domains, outperforming baseline mechanisms. in high-dimensional spaces, we decompose the interpolation process into a sequence of one-dimensional steps and derive a corrected formulation that enforces lp-norm mDP by design. We further explore joint optimization over perturbation distributions and privacy budget allocation across dimensions. Experiments on real-world location datasets demonstrate that our method offers rigorous privacy guarantees and competitive utility in fine-grained domains, outperforming baseline mechanisms.