  Evaluating the causal impacts of possible interventions is crucial for
informing decision-making, especially towards improving access to opportunity.
However, if causal effects are heterogeneous and predictable from covariates,
personalized treatment decisions can improve individual outcomes and contribute
to both efficiency and equity. In practice, however, causal researchers do not
have a single outcome in mind a priori and often collect multiple outcomes of
interest that are noisy estimates of the true target of interest. For example,
in government-assisted social benefit programs, policymakers collect many
outcomes to understand the multidimensional nature of poverty. The ultimate
goal is to learn an optimal treatment policy that in some sense maximizes
multiple outcomes simultaneously. To address such issues, we present a
data-driven dimensionality-reduction methodology for multiple outcomes in the
context of optimal policy learning with multiple objectives. We learn a
low-dimensional representation of the true outcome from the observed outcomes
using reduced rank regression. We develop a suite of estimates that use the
model to denoise observed outcomes, including commonly-used index weightings.
These methods improve estimation error in policy evaluation and optimization,
including on a case study of real-world cash transfer and social intervention
data. Reducing the variance of noisy social outcomes can improve the
performance of algorithmic allocations.
