dorsal/arxiv
View SchemaInterpolation-Based Optimization for Enforcing lp-Norm Metric Differential Privacy in Continuous and Fine-Grained Domains
| Authors | Chenxi Qiu |
|---|---|
| Categories | |
| ArXiv ID | 2601.09946vv1 |
| URL | https://arxiv.org/abs/2601.09946 |
| License | http://creativecommons.org/licenses/by/4.0/ |
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.
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"date_created": "2026-02-17T05:53:24.321000Z",
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"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.\n 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.",
"arxiv_id": "2601.09946",
"authors": [
"Chenxi Qiu"
],
"categories": [
"cs.LG",
"cs.CR"
],
"license": "http://creativecommons.org/licenses/by/4.0/",
"title": "Interpolation-Based Optimization for Enforcing lp-Norm Metric Differential Privacy in Continuous and Fine-Grained Domains",
"url": "https://arxiv.org/abs/2601.09946",
"version": "v1"
},
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