TAN without a burn: Scaling laws of DP-SGD

Tom Sander, Pierre Stock, Alexandre Sablayrolles

Abstract: Differentially Private methods for training Deep Neural Networks (DNNs) have progressed recently, in particular with the use of massive batches and aggregated data augmentations for a large number of steps. These techniques require much more compute than their non-private counterparts, shifting the traditional privacy-accuracy trade-off to a privacy-accuracy-compute trade-off and making hyper-parameter search virtually impossible for realistic scenarios. In this work, we decouple privacy analysis and experimental behavior of noisy training to explore the trade-off with minimal computational requirements. We first use the tools of Rényi Differential Privacy (RDP) to show that the privacy budget, when not overcharged, only depends on the total amount of noise (TAN) injected throughout training. We then derive scaling laws for training models with DP-SGD to optimize hyper-parameters with more than a $100\times$ reduction in computational budget. We apply the proposed method on CIFAR-10 and ImageNet and, in particular, strongly improve the state-of-the-art on ImageNet with a $+9$ points gain in accuracy for a privacy budget $\varepsilon=8$.

Anonymous Url: I certify that there is no URL (e.g., github page) that could be used to find authors’ identity.

No Acknowledgement Section: I certify that there is no acknowledgement section in this submission for double blind review.

Code Of Ethics: I acknowledge that I and all co-authors of this work have read and commit to adhering to the ICLR Code of Ethics

Submission Guidelines: Yes

Please Choose The Closest Area That Your Submission Falls Into: Social Aspects of Machine Learning (eg, AI safety, fairness, privacy, interpretability, human-AI interaction, ethics)

TL;DR: Computationally friendly hyper-parameter search with DP-SGD for new state-of-the-art performance on ImageNet.

Community Implementations: [ 1 code implementation](https://www.catalyzex.com/paper/tan-without-a-burn-scaling-laws-of-dp-sgd/code)