Title: To be private and robust: Differentially Private Optimizers Can Learn Adversarially Robust Models. Abstract: Machine learning models have shone in a variety of domains and attracted increasing attention from both the security and the privacy communities. One important yet worrying question is: will training models under the differential privacy (DP) constraint unfavorably impact on the adversarial robustness? While previous works have postulated that privacy comes at the cost of worse robustness, we give the first theoretical analysis to show that DP models can indeed be robust and accurate, even sometimes more robust than their naturally-trained non-private counterparts. We observe three key factors that influence the privacy-robustness-accuracy tradeoff: (1) hyperparamters for DP optimizers are critical; (2) pre-training on public data significantly mitigates the accuracy and robustness drop; (3) choice of DP optimizers makes a difference. With these factors set properly, we achieve 90\% natural accuracy, 72\% robust accuracy ($+9\%$ than the non-private model) under $l_2(0.5)$ attack, and 69\% robust accuracy ($+16\%$ than the non-private model) with pre-trained SimCLRv2 model under $l_\infty(4/255)$ attack on CIFAR10 with $\epsilon=2$. In fact, we show both theoretically and empirically that DP models are Pareto optimal in terms of accuracy and robustness. Additionally, the robustness of DP models is consistently observed on MNIST, Fashion MNIST and CelebA, with ResNet and Vision Transformer. We believe our encouraging results are a significant step towards training models that are private as well as robust, including deep neural networks.