  The regression discontinuity (RD) design is widely used for program
evaluation with observational data. The primary focus of the existing
literature has been the estimation of the local average treatment effect at the
existing treatment cutoff. In contrast, we consider policy learning under the
RD design. Because the treatment assignment mechanism is deterministic,
learning better treatment cutoffs requires extrapolation. We develop a robust
optimization approach to finding optimal treatment cutoffs that improve upon
the existing ones. We first decompose the expected utility into
point-identifiable and unidentifiable components. We then propose an efficient
doubly-robust estimator for the identifiable parts. To account for the
unidentifiable components, we leverage the existence of multiple cutoffs that
are common under the RD design. Specifically, we assume that the heterogeneity
in the conditional expectations of potential outcomes across different groups
vary smoothly along the running variable. Under this assumption, we minimize
the worst case utility loss relative to the status quo policy. The resulting
new treatment cutoffs have a safety guarantee that they will not yield a worse
overall outcome than the existing cutoffs. Finally, we establish the asymptotic
regret bounds for the learned policy using semi-parametric efficiency theory.
We apply the proposed methodology to empirical and simulated data sets.
