  We investigate the task of estimating the conditional average causal effect
of treatment-dosage pairs from a combination of observational data and
assumptions on the causal relationships in the underlying system. This has been
a longstanding challenge for fields of study such as epidemiology or economics
that require a treatment-dosage pair to make decisions but may not be able to
run randomized trials to precisely quantify their effect and heterogeneity
across individuals. In this paper, we extend (Shalit et al, 2017) to give new
bounds on the counterfactual generalization error in the context of a
continuous dosage parameter which relies on a different approach to defining
counterfactuals and assignment bias adjustment. This result then guides the
definition of new learning objectives that can be used to train representation
learning algorithms for which we show empirically new state-of-the-art
performance results across several benchmark datasets for this problem,
including in comparison to doubly-robust estimation methods.
