  We study off-policy evaluation (OPE) from multiple logging policies, each
generating a dataset of fixed size, i.e., stratified sampling. Previous work
noted that in this setting the ordering of the variances of different
importance sampling estimators is instance-dependent, which brings up a dilemma
as to which importance sampling weights to use. In this paper, we resolve this
dilemma by finding the OPE estimator for multiple loggers with minimum variance
for any instance, i.e., the efficient one. In particular, we establish the
efficiency bound under stratified sampling and propose an estimator achieving
this bound when given consistent $q$-estimates. To guard against
misspecification of $q$-functions, we also provide a way to choose the control
variate in a hypothesis class to minimize variance. Extensive experiments
demonstrate the benefits of our methods' efficiently leveraging of the
stratified sampling of off-policy data from multiple loggers.
