  We study the problem of learning to choose from m discrete treatment options
(e.g., news item or medical drug) the one with best causal effect for a
particular instance (e.g., user or patient) where the training data consists of
passive observations of covariates, treatment, and the outcome of the
treatment. The standard approach to this problem is regress and compare: split
the training data by treatment, fit a regression model in each split, and, for
a new instance, predict all m outcomes and pick the best. By reformulating the
problem as a single learning task rather than m separate ones, we propose a new
approach based on recursively partitioning the data into regimes where
different treatments are optimal. We extend this approach to an optimal
partitioning approach that finds a globally optimal partition, achieving a
compact, interpretable, and impactful personalization model. We develop new
tools for validating and evaluating personalization models on observational
data and use these to demonstrate the power of our novel approaches in a
personalized medicine and a job training application.
