Before revision:  Our approach is based on estimating \theta via an \ell_1-regularized minimization of a sample analog of L_S(\theta, ), plugging in a first-stage estimate , computed on a hold-out sample.
After revision:  Our approach is based on estimating \theta via an \ell_1-regularized minimization of a sample analog of L_S(\theta, that is identified by a class of semiparametric conditional moment restrictions (CMR). We estimate the nonparametric nuisance parameter by modern machine learning methods. Plugging the first-stage estimate , computed on a hold-out sample.