  We provide an adversarial approach to estimating Riesz representers of linear
functionals within arbitrary function spaces. We prove oracle inequalities
based on the localized Rademacher complexity of the function space used to
approximate the Riesz representer and the approximation error. These
inequalities imply fast finite sample mean-squared-error rates for many
function spaces of interest, such as high-dimensional sparse linear functions,
neural networks and reproducing kernel Hilbert spaces. Our approach offers a
new way of estimating Riesz representers with a plethora of recently introduced
machine learning techniques. We show how our estimator can be used in the
context of de-biasing structural/causal parameters in semi-parametric models,
for automated orthogonalization of moment equations and for estimating the
stochastic discount factor in the context of asset pricing.
