Before revision:  Then, we propose doubly robust and efficient estimators for OPE and OPL under a covariate shift by using an estimator of the density ratio between the distributions of the historical and evaluation data  .
After revision:  Then, we propose doubly robust and efficient estimators for OPE and OPL under a covariate shift by using an estimator of the density ratio between the distributions of the historical and evaluation data distributions .