Nov 28, 2022
Differential privacy analysis of randomized learning algorithms typically relies on composition theorems, where the implicit assumption is that the internal state of the iterative algorithm is revealed to the adversary. However, by assuming that the internal state of the algorithm is not revealed, recent works prove a smaller privacy bound for noisy gradient descent (on strongly convex smooth loss functions), compared with composition bounds. In this paper, we significantly improve privacy analysis under the hidden state assumption. We enable taking advantage of privacy amplification by sub-sampling and randomized post-processing, and extend the analysis to “shuffle and partition” and “sample without replacement” stochastic minibatch gradient descent schemes. We prove that, in these settings, our privacy bound is substantially smaller than the composition bounds, notably after many epochs of training (required for learning from high-dimensional data). So, unless the DP algorithm converges fast, our privacy analysis shows that differentially private learning benefits from hidden state privacy analysis. We also empirically show that, given a fixed privacy budget, our analysis enables DP training of image classification models with a better prediction accuracy, compared with prior work.
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