Towards Hyperparameter Transfer for Differentially Private Optimization
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 (μP) 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-μP, a theoretically grounded framework that extends μP 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-μP 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.
Related
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BibTeX
@misc{wang2026towards,
title = {{Towards Hyperparameter Transfer for Differentially Private Optimization}},
author = {Tianze Wang and Zhiqi Bu and Linjun Zhang},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.22976},
eprint = {2610.22976},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.22976},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Towards Hyperparameter Transfer for Differentially Private Optimization
AU - Tianze Wang
AU - Zhiqi Bu
AU - Linjun Zhang
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.22976
UR - https://arxiv.org/abs/2610.22976
AB - 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 (μP) 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-μP, a theoretically grounded framework that extends μP 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-μP 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.
ER -