  Point identification of causal effects requires strong assumptions that are
unreasonable in many practical settings. However, informative bounds on these
effects can often be derived under plausible assumptions. Even when these
bounds are wide or cover null effects, they can guide practical decisions based
on formal decision theoretic criteria. Here we derive new results on optimal
treatment regimes in settings where the effect of interest is bounded. These
results are driven by consideration of superoptimal regimes; we define regimes
that leverage an individual's natural treatment value, which is typically
ignored in the existing literature. We obtain (sharp) bounds for the value
function of superoptimal regimes, and provide performance guarantees relative
to conventional optimal regimes. As a case study, we consider a commonly
studied Marginal Sensitivity Model and illustrate that the superoptimal regime
can be identified when conventional optimal regimes are not. We similarly
illustrate this property in an instrumental variable setting. Finally, we
derive efficient estimators for upper and lower bounds on the superoptimal
value in instrumental variable settings, building on recent results on
covariate adjusted Balke-Pearl bounds. These estimators are applied to study
the effect of prompt ICU admission on survival.
