Balancing Utility and Privacy: Dynamically Private SGD with Random Projection

Abstract: Stochastic optimization is a pivotal enabler in modern machine learning, producing effective models for various tasks. However, several existing works have shown that model parameters and gradient information are susceptible to privacy leakage. Although Differentially Private SGD (DPSGD) addresses privacy concerns, its static noise mechanism impacts the error bounds for model performance. Additionally, with the exponential increase in model parameters, efficient learning of these models using stochastic optimizers has become more challenging. To address these concerns, we introduce the Dynamically Differentially Private Projected SGD (D2P2-SGD) optimizer. In D2P2-SGD, we combine two important ideas: (i) dynamic differential privacy (DDP) with automatic gradient clipping and (ii) random projection with SGD, allowing dynamic adjustment of the tradeoff between utility and privacy of the model. It exhibits provably sub-linear convergence rates across different objective functions, matching the best available rate. The theoretical analysis further suggests that DDP leads to better utility at the cost of privacy, while random projection enables more efficient model learning. Extensive experiments across diverse datasets show that D2P2-SGD remarkably enhances accuracy while maintaining privacy. Our code is available here.