What a Data Release Must Preserve for Off-Policy Evaluation

Kyungbok Lee, Yating Zou, Michael R. Kosorok

In off-policy evaluation, merging decision-time histories that matter differently for a specified policy value or comparison can make that evaluation unidentified, even with observed actions and outcomes and known behavior and target policies. We characterize which distinctions must be preserved: identification holds if and only if the action-specific evaluation weights are constant within each released record, and the coarsest exact release groups histories by these weights. For normalized outcomes, the largest sharp width induced by the release equals a behavior-weighted within-record radius of these weights. The same radius becomes a release-design objective when each record may be refined into at most $m$ categories. The optimum has an exact $m$-center characterization. When behavior does not vary within a released record, we give a finite-data repair algorithm whose maximum evaluation-weight radius is at most twice the finite-data optimum. For a fixed action-outcome distribution within a released record, a distinct sharp-identification problem remains. Under the same condition, the action-specific outcome distributions are identified, and optimizing over their couplings…