  Many algorithms have been recently proposed for causal machine learning. Yet,
there is little to no theory on their quality, especially considering finite
samples. In this work, we propose a theory based on generalization bounds that
provides such guarantees. By introducing a novel change-of-measure inequality,
we are able to tightly bound the model loss in terms of the deviation of the
treatment propensities over the population, which we show can be empirically
limited. Our theory is fully rigorous and holds even in the face of hidden
confounding and violations of positivity. We demonstrate our bounds on
semi-synthetic and real data, showcasing their remarkable tightness and
practical utility.
