DP-SPRT: Differentially Private Sequential Probability Ratio Tests
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arXiv
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| Format: | Preprint |
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2025
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| author | Michel, Thomas Basu, Debabrota Kaufmann, Emilie |
| author_facet | Michel, Thomas Basu, Debabrota Kaufmann, Emilie |
| contents | We revisit Wald's celebrated Sequential Probability Ratio Test for sequential tests of two simple hypotheses, under privacy constraints. We propose DP-SPRT, a wrapper that can be calibrated to achieve desired error probabilities and privacy constraints, addressing a significant gap in previous work. DP-SPRT relies on a private mechanism that processes a sequence of queries and stops after privately determining when the query results fall outside a predefined interval. This OutsideInterval mechanism improves upon naive composition of existing techniques like AboveThreshold, achieving a factor-of-2 privacy improvement and thus potentially benefiting other continual monitoring procedures. We prove generic upper bounds on the error and sample complexity of DP-SPRT that can accommodate various noise distributions based on the practitioner's privacy needs. We exemplify them in two settings: Laplace noise (pure Differential Privacy) and Gaussian noise (Rényi differential privacy). In the former setting, by providing a lower bound on the sample complexity of any $\varepsilon$-DP test with prescribed type I and type II errors, we show that DP-SPRT is near optimal when both errors are small and the two hypotheses are close. Moreover, we conduct an experimental study revealing its good practical performance. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_06377 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | DP-SPRT: Differentially Private Sequential Probability Ratio Tests Michel, Thomas Basu, Debabrota Kaufmann, Emilie Machine Learning Cryptography and Security Statistics Theory We revisit Wald's celebrated Sequential Probability Ratio Test for sequential tests of two simple hypotheses, under privacy constraints. We propose DP-SPRT, a wrapper that can be calibrated to achieve desired error probabilities and privacy constraints, addressing a significant gap in previous work. DP-SPRT relies on a private mechanism that processes a sequence of queries and stops after privately determining when the query results fall outside a predefined interval. This OutsideInterval mechanism improves upon naive composition of existing techniques like AboveThreshold, achieving a factor-of-2 privacy improvement and thus potentially benefiting other continual monitoring procedures. We prove generic upper bounds on the error and sample complexity of DP-SPRT that can accommodate various noise distributions based on the practitioner's privacy needs. We exemplify them in two settings: Laplace noise (pure Differential Privacy) and Gaussian noise (Rényi differential privacy). In the former setting, by providing a lower bound on the sample complexity of any $\varepsilon$-DP test with prescribed type I and type II errors, we show that DP-SPRT is near optimal when both errors are small and the two hypotheses are close. Moreover, we conduct an experimental study revealing its good practical performance. |
| title | DP-SPRT: Differentially Private Sequential Probability Ratio Tests |
| topic | Machine Learning Cryptography and Security Statistics Theory |
| url | https://arxiv.org/abs/2508.06377 |