derive a closed form expression of the minimizer of the squared risk under the Demographic Parity (DP) constraint

We thank all reviewers for their valuable comments. Let us first provide a concise recap of our contributions. We propose an efficient post-processing algorithm (Alg. 1) which can be applied on top of any We highlight that contributions i) and iii) are, up to our knowledge, unique. We now address specific points raised by the reviewers, which will be included in the final version upon acceptance. Let us highlight two key differences between "Wasserstein Fair This is an interesting direction of future research. The main difficulty in such an extension for, e.g., Equalized Odds is due to the conditioning on the Notice also that DP is used in several papers, including Jiang et al. discussed above. Let us disagree that the notion of DP is naive. As stated in the paper (ll. However a form of this assumption is rather classical in non-parametric statistics (see e.g., "Fast learning In our settings As. 4.2 is mostly technical and can be "choice of sigma is left to the user ."