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Shifted Interpolation for Differential Privacy (2403.00278v2)

Published 1 Mar 2024 in cs.LG, cs.CR, math.OC, math.ST, stat.ML, and stat.TH

Abstract: Noisy gradient descent and its variants are the predominant algorithms for differentially private machine learning. It is a fundamental question to quantify their privacy leakage, yet tight characterizations remain open even in the foundational setting of convex losses. This paper improves over previous analyses by establishing (and refining) the "privacy amplification by iteration" phenomenon in the unifying framework of $f$-differential privacy--which tightly captures all aspects of the privacy loss and immediately implies tighter privacy accounting in other notions of differential privacy, e.g., $(\varepsilon,\delta)$-DP and R\'enyi DP. Our key technical insight is the construction of shifted interpolated processes that unravel the popular shifted-divergences argument, enabling generalizations beyond divergence-based relaxations of DP. Notably, this leads to the first exact privacy analysis in the foundational setting of strongly convex optimization. Our techniques extend to many settings: convex/strongly convex, constrained/unconstrained, full/cyclic/stochastic batches, and all combinations thereof. As an immediate corollary, we recover the $f$-DP characterization of the exponential mechanism for strongly convex optimization in Gopi et al. (2022), and moreover extend this result to more general settings.

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References (46)
  1. TensorFlow: a system for large-scale machine learning. In Symposium on Operating Systems Design and Implementation, pages 265–283, 2016.
  2. On the privacy of Noisy Stochastic Gradient Descent for convex optimization. SIAM Journal on Computing, 2024.
  3. Faster high-accuracy log-concave sampling via algorithmic warm starts. In Symposium on Foundations of Computer Science (FOCS), pages 2169–2176, 2023.
  4. Shifted composition I: Harnack and reverse transport inequalities. arXiv preprint arXiv:2311.14520, 2023.
  5. Shifted composition II: Shift Harnack inequalities and curvature upper bounds. arXiv preprint arXiv:2401.00071, 2023.
  6. Deep learning with differential privacy. In Conference on Computer and Communications Security, page 308–318, 2016.
  7. Log-concave and multivariate canonical noise distributions for differential privacy. In Advances in Neural Information Processing Systems, volume 35, pages 34229–34240, 2022.
  8. An introduction to MCMC for machine learning. Machine Learning, 50:5–43, 2003.
  9. Three variants of differential privacy: Lossless conversion and applications. IEEE Journal on Selected Areas in Information Theory, 2(1):208–222, 2021.
  10. Privacy of noisy stochastic gradient descent: More iterations without more privacy loss. In Advances in Neural Information Processing Systems, volume 35, pages 3788–3800, 2022.
  11. Resolving the mixing time of the Langevin algorithm to its stationary distribution for log-concave sampling. In Conference on Learning Theory, volume 195 of Proceedings of Machine Learning Research, pages 2509–2510, 2023.
  12. Harnack inequality and heat kernel estimates on manifolds with curvature unbounded below. Bulletin des Sciences Mathématiques, 130(3):223–233, 2006.
  13. Hypothesis testing interpretations and Renyi differential privacy. In International Conference on Artificial Intelligence and Statistics, volume 108 of Proceedings of Machine Learning Research, pages 2496–2506, 2020.
  14. Deep learning with Gaussian differential privacy. Harvard Data Science Review, 2(3), 2020.
  15. Sampling from a log-concave distribution with projected Langevin Monte Carlo. Discrete & Computational Geometry, 59(4):757–783, 2018.
  16. Private stochastic convex optimization with optimal rates. In Advances in Neural Information Processing Systems, volume 32, 2019.
  17. Concentrated differential privacy: Simplifications, extensions, and lower bounds. In International Conference on Theory of Cryptography, page 635–658, 2016.
  18. Private empirical risk minimization: Efficient algorithms and tight error bounds. In Symposium on Foundations of Computer Science (FOCS), page 464–473, 2014.
  19. Improving the Gaussian mechanism for differential privacy: Analytical calibration and optimal denoising. In International Conference on Machine Learning, volume 80 of Proceedings of Machine Learning Research, pages 394–403, 2018.
  20. Correlated noise provably beats independent noise for differentially private learning. arXiv preprint arXiv:2310.06771, 2023.
  21. Sinho Chewi. Log-concave sampling. 2023. Draft available at https://chewisinho.github.io/.
  22. Differential privacy dynamics of Langevin diffusion and noisy gradient descent. In Advances in Neural Information Processing Systems, volume 34, pages 14771–14781, 2021.
  23. Calibrating noise to sensitivity in private data analysis. In Theory of cryptography, volume 3876 of Lecture Notes in Computuer Science, pages 265–284. Springer, Berlin, 2006.
  24. The algorithmic foundations of differential privacy. Foundations and Trends® in Theoretical Computer Science, 9(3–4):211–407, 2014.
  25. Gaussian differential privacy. Journal of the Royal Statistical Society, Series B, Statistical Methodology, 84(1):3–54, 2022. With discussions and a reply by the authors.
  26. Privacy amplification by iteration. In 59th Annual IEEE Symposium on Foundations of Computer Science—FOCS 2018, pages 521–532. IEEE Computer Soc., Los Alamitos, CA, 2018.
  27. Faster differentially private convex optimization via second-order methods. arXiv preprint arXiv:2305.13209, 2023.
  28. Private convex optimization via exponential mechanism. In Conference on Learning Theory, volume 178 of Proceedings of Machine Learning Research, pages 1948–1989, 2022.
  29. Numerical composition of differential privacy. In Advances in Neural Information Processing Systems, volume 34, pages 11631–11642, 2021.
  30. What can we learn privately? SIAM Journal on Computing, 40(3):793–826, 2011.
  31. The composition theorem for differential privacy. IEEE Transactions on Information Theory, 63(6):4037–4049, 2017.
  32. MNIST handwritten digit database. ATT Labs [Online]. Available: http://yann.lecun.com/exdb/mnist, 2, 2010.
  33. Michel Ledoux. Concentration of measure and logarithmic Sobolev inequalities. In Jacques Azéma, Michel Émery, Michel Ledoux, and Marc Yor, editors, Séminaire de Probabilités XXXIII, pages 120–216, Berlin, Heidelberg, 1999. Springer Berlin Heidelberg.
  34. Jun S. Liu. Monte Carlo strategies in scientific computing, volume 75. Springer, 2001.
  35. Differential privacy without sensitivity. In Advances in Neural Information Processing Systems, volume 29, 2016.
  36. Ilya Mironov. Rényi differential privacy. In Computer Security Foundations Symposium, pages 263–275, 2017.
  37. Mechanism design via differential privacy. In Foundations of Computer Science (FOCS), pages 94–103, 2007.
  38. Pytorch: An imperative style, high-performance deep learning library. In Advances in Neural Information Processing Systems, volume 32, 2019.
  39. Monte Carlo statistical methods, volume 2. Springer, 1999.
  40. Feng-Yu Wang. Harnack inequalities for stochastic partial differential equations, volume 1332. Springer, 2013.
  41. Feng-Yu Wang. Analysis for diffusion processes on Riemannian manifolds, volume 18. World Scientific, 2014.
  42. Unified enhancement of privacy bounds for mixture mechanisms via f𝑓fitalic_f-differential privacy. In Advances in Neural Information Processing Systems, volume 36, 2023.
  43. A statistical framework for differential privacy. Journal of the American Statistical Association, 105(489):375–389, 2010.
  44. Differentially private learning needs hidden state (or much faster convergence). In Advances in Neural Information Processing Systems, volume 35, pages 703–715, 2022.
  45. Sharp composition bounds for Gaussian differential privacy via Edgeworth expansion. In International Conference on Machine Learning, volume 119 of Proceedings of Machine Learning Research, pages 11420–11435, 2020.
  46. Optimal accounting of differential privacy via characteristic function. In International Conference on Artificial Intelligence and Statistics, volume 151 of Proceedings of Machine Learning Research, pages 4782–4817, 2022.
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