consideration of whether or not the empirical process term represents the dominant error term, or whether the second-order remainder that appears due to the non-linearity of the value parameter represents the dominant error term. In restricted, semiparametric models, we suspect that, depending on the underlying margin, an inefficient estimator of the value may yield a faster rate of regret decay than an efficient estimator. Despite this surprising phenomenon, we continue to advocate the use of first-order efficient value estimators. Alex Luedtke gratefully acknowledges the support of the New Development Fund of the Fred Hutchinson Cancer Research Center. Antoine Chambaz acknowledges the support of the French Agence Nationale de la Recherche (ANR), under grant ANR-13-BS01-0005 (project SPADRO) and that this research has been conducted as part of the project Labex MME-DII (ANR11-LBX-0023-01). 22 Acknowledgements