Review for NeurIPS paper: Fair regression via plug-in estimator and recalibration with statistical guarantees

Summary and Contributions: This paper provides a new algorithm to train a regression function subject to a demographic parity like fairness constraint. The proposed approach constructs a plug-in estimator by first training an unconstrained regression function using labeled data and calibrate the model to satisfy the fairness constraint using unlabeled data. The final model is a "regression function with discrete outputs". The authors show convergence rates to the optimal fair regression model, and demonstrate competitive empirical performance compared to previous approaches for fair regression. I'm still of the opinion that the technical gap I pointed out is an important one, and that the analysis would have been much more complete and satisfying had the guarantees for the optimization algorithm been on the gradients of the dual objective.