PAnDA: Rethinking Metric Differential Privacy Optimization at Scale with Anchor-Based Approximation
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866916944995680256 |
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| author | Liu, Ruiyao Qiu, Chenxi |
| author_facet | Liu, Ruiyao Qiu, Chenxi |
| contents | Metric Differential Privacy (mDP) extends the local differential privacy (LDP) framework to metric spaces, enabling more nuanced privacy protection for data such as geo-locations. However, existing mDP optimization methods, particularly those based on linear programming (LP), face scalability challenges due to the quadratic growth in decision variables. In this paper, we propose Perturbation via Anchor-based Distributed Approximation (PAnDA), a scalable two-phase framework for optimizing metric differential privacy (mDP). To reduce computational overhead, PAnDA allows each user to select a small set of anchor records, enabling the server to solve a compact linear program over a reduced domain. We introduce three anchor selection strategies, exponential decay (PAnDA-e), power-law decay (PAnDA-p), and logistic decay (PAnDA-l), and establish theoretical guarantees under a relaxed privacy notion called probabilistic mDP (PmDP). Experiments on real-world geo-location datasets demonstrate that PAnDA scales to secret domains with up to 5,000 records, two times larger than prior LP-based methods, while providing theoretical guarantees for both privacy and utility. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_08720 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | PAnDA: Rethinking Metric Differential Privacy Optimization at Scale with Anchor-Based Approximation Liu, Ruiyao Qiu, Chenxi Cryptography and Security Metric Differential Privacy (mDP) extends the local differential privacy (LDP) framework to metric spaces, enabling more nuanced privacy protection for data such as geo-locations. However, existing mDP optimization methods, particularly those based on linear programming (LP), face scalability challenges due to the quadratic growth in decision variables. In this paper, we propose Perturbation via Anchor-based Distributed Approximation (PAnDA), a scalable two-phase framework for optimizing metric differential privacy (mDP). To reduce computational overhead, PAnDA allows each user to select a small set of anchor records, enabling the server to solve a compact linear program over a reduced domain. We introduce three anchor selection strategies, exponential decay (PAnDA-e), power-law decay (PAnDA-p), and logistic decay (PAnDA-l), and establish theoretical guarantees under a relaxed privacy notion called probabilistic mDP (PmDP). Experiments on real-world geo-location datasets demonstrate that PAnDA scales to secret domains with up to 5,000 records, two times larger than prior LP-based methods, while providing theoretical guarantees for both privacy and utility. |
| title | PAnDA: Rethinking Metric Differential Privacy Optimization at Scale with Anchor-Based Approximation |
| topic | Cryptography and Security |
| url | https://arxiv.org/abs/2509.08720 |