Adversarial Monte Carlo Meta-Learning of Conditional Average Treatment Effects
Alex R. Luedtke, Incheoul Chung · 2024
Traditionally, statistical procedures have been derived via analytic calculations whose validity often relies on the sample size growing to infinity. In this chapter, we describe how to use deep adversarial learning to numerically construct a statistical procedure that performs well even in small samples. More concretely, we frame the meta-learning of conditional average treatment effect estimators as a search for an optimal strategy in a two-player game. In this game, Nature selects a prior over distributions that generate labeled data consisting of covariates, treatment, and an associated outcome, and the Estimator observes data sampled from a distribution drawn from this prior. The Estimator&s;s objective is to learn a function that maps from a new feature to an estimate of the conditional average treatment effect. We argue that, under reasonable conditions, the Estimator has an optimal strategy that is equivariant to shifts and rescalings of the outcome, and is invariant to permutations of the observations and to shifts, rescalings, and permutations of the features. We introduce a neural network architecture that satisfies these properties.