Before revision:   To control in a data-driven way for  potentially high dimensional pre-treatment covariatesthat motivate the selection-on-observables assumptions , we adapt the double machine learning framework  to sample selection problems.
After revision:  We also consider dynamic confounding, meaning that covariates that jointly affect sample selection and the outcome may (at least partly) be influenced by the treatment. To control in a data-driven way for potentially high dimensional pre-treatment covariatesthat motivate the selection-on-observables assumptions , we adapt the double machine learning framework to sample selection problems.