  Biases in observational data of treatments pose a major challenge to
estimating expected treatment outcomes in different populations. An important
technique that accounts for these biases is reweighting samples to minimize the
discrepancy between treatment groups. We present a novel reweighting approach
that uses bi-level optimization to alternately train a discriminator to
minimize classification error, and a balancing weights generator that uses
exponentiated gradient descent to maximize this error. This approach borrows
principles from generative adversarial networks (GANs) to exploit the power of
classifiers for measuring two-sample divergence. We provide theoretical results
for conditions in which the estimation error is bounded by two factors: (i) the
discrepancy measure induced by the discriminator; and (ii) the weights
variability. Experimental results on several benchmarks comparing to previous
state-of-the-art reweighting methods demonstrate the effectiveness of this
approach in estimating causal effects.
