  Many practical problems involve estimating low dimensional statistical
quantities with high-dimensional models and datasets. Several approaches
address these estimation tasks based on the theory of influence functions, such
as debiased/double ML or targeted minimum loss estimation. This paper
introduces \textit{Monte Carlo Efficient Influence Functions} (MC-EIF), a fully
automated technique for approximating efficient influence functions that
integrates seamlessly with existing differentiable probabilistic programming
systems. MC-EIF automates efficient statistical estimation for a broad class of
models and target functionals that would previously require rigorous custom
analysis. We prove that MC-EIF is consistent, and that estimators using MC-EIF
achieve optimal $\sqrt{N}$ convergence rates. We show empirically that
estimators using MC-EIF are at parity with estimators using analytic EIFs.
Finally, we demonstrate a novel capstone example using MC-EIF for optimal
portfolio selection.
