The Cost of Shuffling in Private Gradient Based Optimization

• URL: http://arxiv.org/abs/2502.03652v1
• Date: Wed, 05 Feb 2025 22:30:00 GMT
• Title: The Cost of Shuffling in Private Gradient Based Optimization
• Authors: Shuli Jiang, Pranay Sharma, Zhiwei Steven Wu, Gauri Joshi,
• Abstract summary: We show that data shuffling results in worse empirical excess risk for textitDP-ShuffleG compared to DP-SGD. We propose textitInterleaved-ShuffleG, a hybrid approach that integrates public data samples in private optimization.
• Score: 40.31928071333575
• License:
• Abstract: We consider the problem of differentially private (DP) convex empirical risk minimization (ERM). While the standard DP-SGD algorithm is theoretically well-established, practical implementations often rely on shuffled gradient methods that traverse the training data sequentially rather than sampling with replacement in each iteration. Despite their widespread use, the theoretical privacy-accuracy trade-offs of private shuffled gradient methods (\textit{DP-ShuffleG}) remain poorly understood, leading to a gap between theory and practice. In this work, we leverage privacy amplification by iteration (PABI) and a novel application of Stein's lemma to provide the first empirical excess risk bound of \textit{DP-ShuffleG}. Our result shows that data shuffling results in worse empirical excess risk for \textit{DP-ShuffleG} compared to DP-SGD. To address this limitation, we propose \textit{Interleaved-ShuffleG}, a hybrid approach that integrates public data samples in private optimization. By alternating optimization steps that use private and public samples, \textit{Interleaved-ShuffleG} effectively reduces empirical excess risk. Our analysis introduces a new optimization framework with surrogate objectives, adaptive noise injection, and a dissimilarity metric, which can be of independent interest. Our experiments on diverse datasets and tasks demonstrate the superiority of \textit{Interleaved-ShuffleG} over several baselines.

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