  Differential Privacy (DP) provides a formal privacy guarantee preventing
adversaries with access to a machine learning model from extracting information
about individual training points. Differentially Private Stochastic Gradient
Descent (DP-SGD), the most popular DP training method for deep learning,
realizes this protection by injecting noise during training. However previous
works have found that DP-SGD often leads to a significant degradation in
performance on standard image classification benchmarks. Furthermore, some
authors have postulated that DP-SGD inherently performs poorly on large models,
since the norm of the noise required to preserve privacy is proportional to the
model dimension. In contrast, we demonstrate that DP-SGD on over-parameterized
models can perform significantly better than previously thought. Combining
careful hyper-parameter tuning with simple techniques to ensure signal
propagation and improve the convergence rate, we obtain a new SOTA without
extra data on CIFAR-10 of 81.4% under (8, 10^{-5})-DP using a 40-layer
Wide-ResNet, improving over the previous SOTA of 71.7%. When fine-tuning a
pre-trained NFNet-F3, we achieve a remarkable 83.8% top-1 accuracy on ImageNet
under (0.5, 8*10^{-7})-DP. Additionally, we also achieve 86.7% top-1 accuracy
under (8, 8 \cdot 10^{-7})-DP, which is just 4.3% below the current non-private
SOTA for this task. We believe our results are a significant step towards
closing the accuracy gap between private and non-private image classification.
