  The unit selection problem aims to find objects, called units, that optimize
a causal objective function which describes the objects' behavior in a causal
context (e.g., selecting customers who are about to churn but would most likely
change their mind if encouraged). While early studies focused mainly on
bounding a specific class of counterfactual objective functions using data,
more recent work allows one to find optimal units exactly by reducing the
causal objective to a classical objective on a meta-model, and then applying a
variant of the classical Variable Elimination (VE) algorithm to the meta-model
-- assuming a fully specified causal model is available. In practice, however,
finding optimal units using this approach can be very expensive because the
used VE algorithm must be exponential in the constrained treewidth of the
meta-model, which is larger and denser than the original model. We address this
computational challenge by introducing a new approach for unit selection that
is not necessarily limited by the constrained treewidth. This is done through
compiling the meta-model into a special class of tractable arithmetic circuits
that allows the computation of optimal units in time linear in the circuit
size. We finally present empirical results on random causal models that show
order-of-magnitude speedups based on the proposed method for solving unit
selection.
