Revisiting Privacy-Utility Trade-off for DP Training with Pre-existing Knowledge

Abstract: Differential privacy (DP) provides a provable framework for protecting individuals by customizing a random mechanism over a privacy-sensitive dataset. Deep learning models have demonstrated privacy risks in model exposure as an established learning model unintentionally records membership-level privacy leakage. Differentially private stochastic gradient descent (DP-SGD) has been proposed to safeguard training individuals by adding random Gaussian noise to gradient updates in the backpropagation. Researchers identify that DP-SGD causes utility loss since the injected homogeneous noise can alter the gradient updates calculated at each iteration. Namely, all elements in the gradient are contaminated regardless of their importance in updating model parameters. In this work, we argue that the utility can be optimized by involving the heterogeneity of the the injected noise. Consequently, we propose a generic differential privacy framework with heterogeneous noise (DP-Hero) by defining a heterogeneous random mechanism to abstract its property. The insight of DP-Hero is to leverage the knowledge encoded in the previously trained model to guide the subsequent allocation of noise heterogeneity, thereby leveraging the statistical perturbation and achieving enhanced utility. Atop DP-Hero, we instantiate a heterogeneous version of DP-SGD, where the noise injected into gradients is heterogeneous and guided by prior-established model parameters. We conduct comprehensive experiments to verify and explain the effectiveness of the proposed DP-Hero, showing improved training accuracy compared with state-of-the-art works. Broadly, we shed light on improving the privacy-utility space by learning the noise guidance from the pre-existing leaked knowledge encoded in the previously trained model, showing a different perspective of understanding the utility-improved DP training.