  The off-policy learning paradigm allows for recommender systems and general
ranking applications to be framed as decision-making problems, where we aim to
learn decision policies that optimize an unbiased offline estimate of an online
reward metric. With unbiasedness comes potentially high variance, and prevalent
methods exist to reduce estimation variance. These methods typically make use
of control variates, either additive (i.e., baseline corrections or doubly
robust methods) or multiplicative (i.e., self-normalisation). Our work unifies
these approaches by proposing a single framework built on their equivalence in
learning scenarios. The foundation of our framework is the derivation of an
equivalent baseline correction for all of the existing control variates.
Consequently, our framework enables us to characterize the variance-optimal
unbiased estimator and provide a closed-form solution for it. This optimal
estimator brings significantly improved performance in both evaluation and
learning, and minimizes data requirements. Empirical observations corroborate
our theoretical findings.
