On the Convergence and Calibration of Deep Learning with Differential Privacy

Differentially private (DP) training preserves the data privacy usually at the cost of slower convergence (and thus lower accuracy), as well as more severe mis-calibration than its non-private counterpart. To analyze the convergence of DP training, we formulate a continuous time analysis through the...

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Bibliographic Details
Published inarXiv.org
Main Authors Bu, Zhiqi, Wang, Hua, Dai, Zongyu, Long, Qi
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 19.06.2023
Subjects
Classifiers
Computer architecture
Convergence
Deep learning
Gradient flow
Machine learning
Neural networks
Noise levels
Privacy
Training
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Summary:Differentially private (DP) training preserves the data privacy usually at the cost of slower convergence (and thus lower accuracy), as well as more severe mis-calibration than its non-private counterpart. To analyze the convergence of DP training, we formulate a continuous time analysis through the lens of neural tangent kernel (NTK), which characterizes the per-sample gradient clipping and the noise addition in DP training, for arbitrary network architectures and loss functions. Interestingly, we show that the noise addition only affects the privacy risk but not the convergence or calibration, whereas the per-sample gradient clipping (under both flat and layerwise clipping styles) only affects the convergence and calibration. Furthermore, we observe that while DP models trained with small clipping norm usually achieve the best accurate, but are poorly calibrated and thus unreliable. In sharp contrast, DP models trained with large clipping norm enjoy the same privacy guarantee and similar accuracy, but are significantly more \textit{calibrated}. Our code can be found at \url{https://github.com/woodyx218/opacus_global_clipping}.
ISSN:2331-8422