  We provide adaptive inference methods, based on $\ell_1$ regularization, for
regular (semi-parametric) and non-regular (nonparametric) linear functionals of
the conditional expectation function. Examples of regular functionals include
average treatment effects, policy effects, and derivatives. Examples of
non-regular functionals include average treatment effects, policy effects, and
derivatives conditional on a covariate subvector fixed at a point. We construct
a Neyman orthogonal equation for the target parameter that is approximately
invariant to small perturbations of the nuisance parameters. To achieve this
property, we include the Riesz representer for the functional as an additional
nuisance parameter. Our analysis yields weak ``double sparsity robustness'':
either the approximation to the regression or the approximation to the
representer can be ``completely dense'' as long as the other is sufficiently
``sparse''. Our main results are non-asymptotic and imply asymptotic uniform
validity over large classes of models, translating into honest confidence bands
for both global and local parameters.
