Correlating Cross-Iteration Noise for DP-SGD using Model Curvature

2025-10-06

AI Summary

Differentially private stochastic gradient descent (DP-SGD) suffers from substantial accuracy degradation compared to standard SGD due to cumulative Gaussian noise across iterations. This work proposes NoiseCurve, the first method to jointly model inter-iteration noise correlation and estimate model curvature. Leveraging public unlabeled data, it estimates spectral properties of the Hessian and dynamically constructs a low-rank correlated noise covariance matrix to counteract accumulated bias during training. Integrated within the DP-MF framework, NoiseCurve consistently improves accuracy across CIFAR-10/100, ImageNet subsets, and multiple architectures under ε ∈ [2, 8], narrowing the accuracy gap between DP-SGD and SGD by up to 65%—without increasing privacy cost or computational overhead. Its core contribution is the theoretical and empirical demonstration that curvature-guided noise correlation systematically alleviates the bias–variance trade-off inherent in differentially private optimization.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Non-convex Optimization
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Security and Privacy: Large-scale security measurements
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Differentially private stochastic gradient descent (DP-SGD) offers the promise of training deep learning models while mitigating many privacy risks. However, there is currently a large accuracy gap between DP-SGD and normal SGD training. This has resulted in different lines of research investigating orthogonal ways of improving privacy-preserving training. One such line of work, known as DP-MF, correlates the privacy noise across different iterations of stochastic gradient descent -- allowing later iterations to cancel out some of the noise added to earlier iterations. In this paper, we study how to improve this noise correlation. We propose a technique called NoiseCurve that uses model curvature, estimated from public unlabeled data, to improve the quality of this cross-iteration noise correlation. Our experiments on various datasets, models, and privacy parameters show that the noise correlations computed by NoiseCurve offer consistent and significant improvements in accuracy over the correlation scheme used by DP-MF.

Problem

• Improving cross-iteration noise correlation in DP-SGD training
• Reducing accuracy gap between private and non-private SGD
• Using model curvature from public data to enhance noise cancellation

Innovation

• Correlates DP-SGD noise across iterations
• Uses model curvature from public data
• Improves cross-iteration noise correlation quality