Before revision:  We also show that Lasso based, cross-fit, debiased machine learning estimators are asymptotically efficient under these conditions. In addition we show efficiency of an estimator without cross-fitting when the functional depends on the regressors and the regressionsparse approximation rate satisfies \xi_{1 1/ 2.
After revision:  We also show that Lasso based, cross-fit, debiased machine learning estimators are asymptotically efficient under minimal conditions. These estimators use no cross-fitting when the functional depends on the regressors and the regressionsparse approximation rate satisfies \xi_{1 1/ 2.