Automatic Debiased Machine Learning with Generic Machine Learning for Static and Dynamic Causal Parameters
Abstract: We propose a method for automated debiased machine learning in static and dynamic treatment regimes, that allows for generic machine learning estimators to be used for automatically constructing the debiasing term. As a special case, we show that the multiply robust formula for the dynamic treatment regime with discrete treatments can be re-stated in terms of a recursive Riesz representer characterization of nested mean regressions. We then propose a recursive Riesz representer M-estimation learning algorithm that estimates de-biasing corrections without the need to characterize how the correction terms look like. Our approach defines a sequence of loss minimization problems, whose minimizers are the mulitpliers of the de-biasing correction, hence circumventing the need for solving auxiliary propensity models and directly optimizing for the mean squared error of the target de-biasing correction. We provide finite sample high probability mean squared error bounds for our recursive Riesz estimation process via the use of localized Rademacher complexities.