Analyzing and Optimizing Perturbation of DP-SGD Geometrically
Keywords: Differential Privacy, Stochastic Gradient Descent, Deep Learning, Efficiency Analysis and Enhancement
TL;DR: Taking advantage of the geometric property of gradient for improvement of DP-SGD
Abstract: Differential privacy (DP) has become a prevalent privacy model in
a wide range of machine learning tasks, especially after the debut
of DP-SGD. However, DP-SGD, which directly perturbs gradients
in the training iterations, fails to mitigate the negative impacts of
noise on gradient direction. As a result, DP-SGD is often inefficient.
Although various solutions (e.g., clipping to reduce the sensitivity
of gradients and amplifying privacy bounds to save privacy budgets)
are proposed to trade privacy for model efficiency, the root cause of
its inefficiency is yet unveiled.
In this work, we first generalize DP-SGD and theoretically derive
the impact of DP noise on the training process. Our analysis reveals
that, in terms of a perturbed gradient, only the noise on a direction
has eminent impact on the model efficiency while that on magnitude
can be mitigated by optimization techniques, i.e., fine-tuning gradient
clipping and learning rate. Besides, we confirm that traditional
DP introduces biased noise on the direction when adding unbiased
noise to the gradient itself. Overall, the perturbation of DP-SGD is
actually sub-optimal from a geometric perspective. Motivated by
this, we design a geometric perturbation strategy GeoDP within the
DP framework, which perturbs the direction and the magnitude of a
gradient, respectively. By directly reducing the noise on the direction,
GeoDP mitigates the negative impact of DP noise on model
efficiency with the same DP guarantee. Extensive experiments on
two public datasets (i.e., MNIST and CIFAR-10), one synthetic
dataset and three prevalent models (i.e., Logistic Regression, CNN
and ResNet) confirm the effectiveness and generality of our strategy.
Supplementary Material: pdf
Primary Area: alignment, fairness, safety, privacy, and societal considerations
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Submission Number: 2696
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