Title: Interval-based Offline Policy Evaluation without Sufficient Exploration or Realizability. Abstract: We study the problem of offline policy evaluation (OPE),
where the goal is to estimate the value of given decision-making policy without interacting with the actual environment.
In particular, we consider the interval-based OPE, where the output is an interval rather than a point, indicating the uncertainty of the evaluation.
The interval-based estimation is especially important in OPE since, 
when the data coverage is insufficient relative to the complexity of the environmental model,
any OPE method can be biased even with infinite sample size.
In this paper, we characterize the worst case of such irreducible bias, called the *minimax bias*, in terms of the discrepancy between the target policy and the data-sampling distribution,
and show that the marginal-importance-sampling (MIS) estimator achieves the minimax bias with an appropriate importance-weight function.
Motivated with this result, we then propose a new interval-based MIS estimator that asymptotically achieves the minimax bias.