  We consider learning personalized assignments to one of many treatment arms
from a randomized controlled trial. Standard methods that estimate
heterogeneous treatment effects separately for each arm may perform poorly in
this case due to excess variance. We instead propose methods that pool
information across treatment arms: First, we consider a regularized
forest-based assignment algorithm based on greedy recursive partitioning that
shrinks effect estimates across arms. Second, we augment our algorithm by a
clustering scheme that combines treatment arms with consistently similar
outcomes. In a simulation study, we compare the performance of these approaches
to predicting arm-wise outcomes separately, and document gains of directly
optimizing the treatment assignment with regularization and clustering. In a
theoretical model, we illustrate how a high number of treatment arms makes
finding the best arm hard, while we can achieve sizable utility gains from
personalization by regularized optimization.
