  Estimation of individual treatment effects is commonly used as the basis for
contextual decision making in fields such as healthcare, education, and
economics. However, it is often sufficient for the decision maker to have
estimates of upper and lower bounds on the potential outcomes of decision
alternatives to assess risks and benefits. We show that, in such cases, we can
improve sample efficiency by estimating simple functions that bound these
outcomes instead of estimating their conditional expectations, which may be
complex and hard to estimate. Our analysis highlights a trade-off between the
complexity of the learning task and the confidence with which the learned
bounds hold. Guided by these findings, we develop an algorithm for learning
upper and lower bounds on potential outcomes which optimize an objective
function defined by the decision maker, subject to the probability that bounds
are violated being small. Using a clinical dataset and a well-known causality
benchmark, we demonstrate that our algorithm outperforms baselines, providing
tighter, more reliable bounds.
