  We study minimax methods for off-policy evaluation (OPE) using value
functions and marginalized importance weights. Despite that they hold promises
of overcoming the exponential variance in traditional importance sampling,
several key problems remain:
  (1) They require function approximation and are generally biased. For the
sake of trustworthy OPE, is there anyway to quantify the biases?
  (2) They are split into two styles ("weight-learning" vs "value-learning").
Can we unify them?
  In this paper we answer both questions positively. By slightly altering the
derivation of previous methods (one from each style; Uehara et al., 2020), we
unify them into a single value interval that comes with a special type of
double robustness: when either the value-function or the importance-weight
class is well specified, the interval is valid and its length quantifies the
misspecification of the other class. Our interval also provides a unified view
of and new insights to some recent methods, and we further explore the
implications of our results on exploration and exploitation in off-policy
policy optimization with insufficient data coverage.
