Optimal Guarantees for Auditing Rényi Differentially Private Machine Learning
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| Format: | Preprint |
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2026
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| author | Kim, Benjamin D. Varshney, Lav R. Alabi, Daniel |
| author_facet | Kim, Benjamin D. Varshney, Lav R. Alabi, Daniel |
| contents | We study black-box auditing for machine learning algorithms that claim R \ 'enyi differential privacy (RDP) guarantees. We introduce an auditing framework, based on hypothesis testing, that directly estimates Rényi divergence between neighboring executions using the Donsker-Varadhan (DV) variational estimator. Our analysis yields explicit and non-asymptotic confidence intervals for RDP auditing via class-restricted DV estimators, separating statistical estimation error from algorithmic privacy leakage. We prove matching minimax lower bounds showing that, up to logarithmic factors, our sample-complexity guarantees are information-theoretically optimal, thereby establishing the first optimal guarantees for auditing RDP via DV estimators. Empirically, we instantiate our framework for auditing DP-SGD in a fully black-box setting. Across MNIST and CIFAR-10, and over a wide range of privacy regimes, our auditors produce a strong overall improvement on empirical RDP lower bounds compared to prior state-of-the-art black-box methods especially at small and moderate Rényi orders where accurate auditing is most challenging. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_21938 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal Guarantees for Auditing Rényi Differentially Private Machine Learning Kim, Benjamin D. Varshney, Lav R. Alabi, Daniel Machine Learning Cryptography and Security Information Theory We study black-box auditing for machine learning algorithms that claim R \ 'enyi differential privacy (RDP) guarantees. We introduce an auditing framework, based on hypothesis testing, that directly estimates Rényi divergence between neighboring executions using the Donsker-Varadhan (DV) variational estimator. Our analysis yields explicit and non-asymptotic confidence intervals for RDP auditing via class-restricted DV estimators, separating statistical estimation error from algorithmic privacy leakage. We prove matching minimax lower bounds showing that, up to logarithmic factors, our sample-complexity guarantees are information-theoretically optimal, thereby establishing the first optimal guarantees for auditing RDP via DV estimators. Empirically, we instantiate our framework for auditing DP-SGD in a fully black-box setting. Across MNIST and CIFAR-10, and over a wide range of privacy regimes, our auditors produce a strong overall improvement on empirical RDP lower bounds compared to prior state-of-the-art black-box methods especially at small and moderate Rényi orders where accurate auditing is most challenging. |
| title | Optimal Guarantees for Auditing Rényi Differentially Private Machine Learning |
| topic | Machine Learning Cryptography and Security Information Theory |
| url | https://arxiv.org/abs/2605.21938 |