  Off-policy evaluation (OPE) in both contextual bandits and reinforcement
learning allows one to evaluate novel decision policies without needing to
conduct exploration, which is often costly or otherwise infeasible. The
problem's importance has attracted many proposed solutions, including
importance sampling (IS), self-normalized IS (SNIS), and doubly robust (DR)
estimates. DR and its variants ensure semiparametric local efficiency if
Q-functions are well-specified, but if they are not they can be worse than both
IS and SNIS. It also does not enjoy SNIS's inherent stability and boundedness.
We propose new estimators for OPE based on empirical likelihood that are always
more efficient than IS, SNIS, and DR and satisfy the same stability and
boundedness properties as SNIS. On the way, we categorize various properties
and classify existing estimators by them. Besides the theoretical guarantees,
empirical studies suggest the new estimators provide advantages.
