🤖 AI Summary
This work addresses the high computational cost and poor scalability of existing optimization-based metric differential privacy (mDP) mechanisms in continuous, fine-grained domains, which stem from the need to construct dense perturbation matrices and enforce pointwise constraints. To overcome these limitations, we propose the first framework that integrates interpolation with mDP: perturbation distributions are optimized only at sparse anchor points, and distributions at non-anchor locations are generated via one-dimensional stepwise decomposition and log-convex interpolation. A correction formula is introduced to rigorously satisfy ℓp-norm mDP constraints, while jointly optimizing both the perturbation distributions and the allocation of privacy budgets across dimensions. Experiments on real-world location datasets demonstrate that our approach achieves strong privacy guarantees without sacrificing utility, significantly outperforming existing baselines in fine-grained domains.
📝 Abstract
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.