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arXiv · 2610.22976

Towards Hyperparameter Transfer for Differentially Private Optimization

Tianze Wang·Zhiqi Bu·Linjun Zhang
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Abstract

Scaling laws and hyperparameter tuning remain central challenges in training large-scale models, particularly under differential privacy (DP), where optimization is further complicated by noise injection and per-sample gradient clipping. While Maximal Update Parametrization ($μ$P) allows for zero-shot hyperparameter transfer in standard training, we show that it fails under DP constraints due to the distinct spectral properties of high-dimensional noise versus low-rank gradients. In this work, we introduce DP-$μ$P, a theoretically grounded framework that extends $μ$P to the privacy-preserving setting. By analyzing the interaction between gradient clipping, noise injection, and feature learning, we derive a Signal-to-Noise Ratio (SNR) condition that governs layer-wise learning rate scaling. Combining this with our proposed spectral scaling formulation, we provide specific scaling rules for DP-SGD, DP-Adam, and DP-Muon optimizers. Empirically, we demonstrate that DP-$μ$P enables effective zero-shot transfer of learning rates across model widths on diverse architectures (MLP, ViT, GPT-2), matching or exceeding the performance of individually tuned baselines while significantly reducing computational costs.

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BibTeXRIS

Tianze Wang, Zhiqi Bu, Linjun Zhang. 2026-10-16. Towards Hyperparameter Transfer for Differentially Private Optimization. https://arxiv.org/abs/2610.22976

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