1. The main (and only) theoretical result in the paper provides utility guarantees for the proposed algorithm only when the features and noise are Gaussian. This is a strong requirement on the data, especially given that previous algorithms don’t need this assumption as well. Moreover, the authors should compare the rates achieved by their procedure to existing rates in the literature. 2. Experiments: the experimental results in the paper don’t provide a convincing argument for their algorithms. First, all of the experiments are done over synthetic data. Moreover, the authors only consider low-dimensional datasets where d<30 and therefore it is not clear if the same improvements hold for high-dimensional problems. Finally, it is not clear whether the authors used any hyper-parameter tuning for DP-GD (or DP-SGD); this could result in significantly better results for DP-GD. 3. Writing: I encourage the authors to improve the writing in this paper. For example, the introduction could use more work on setting up the problem, stating the main results and comparing to previous work, before moving on to present the algorithm (which is done too soon in the current version). More:
Typo (first sentence): “is a standard”
First paragraph in page 4 has m. What is m? Should that be n?
1. The main (and only) theoretical result in the paper provides utility guarantees for the proposed algorithm only when the features and noise are Gaussian. This is a strong requirement on the data, especially given that previous algorithms don’t need this assumption as well. Moreover, the authors should compare the rates achieved by their procedure to existing rates in the literature.