Review for NeurIPS paper: Sharp uniform convergence bounds through empirical centralization

Weaknesses: The authors consider the supremum of absolute deviation \sup_f \hat{E}_x[f]-E_D[f] . In statistical learning theory, it suffices to estimate \sup_{f}[E_D[f]-\hat{E}_x[f]], i.e., there is no absolute value. Therefore, the results in this paper may not be interesting since centralization does not help for a smaller complexity that is sufficient for generalization. The centralization in terms of expectation has been considered in the literature for both Rademacher averages and variances. This paper extends this centralization to empirical centralization.