The recently proposed distribution correction estimation (DICE) family of estimators has advanced the state of the art in off-policy evaluation from behavior-agnostic data. While these estimators all perform some form of stationary distribution correction, they arise from different derivations and objective functions. In this paper, we unify these estimators as regularized Lagrangians of the same linear program. The unification allows us to expand the space of DICE estimators to new alternatives that demonstrate improved performance. More importantly, by analyzing the expanded space of estimators both mathematically and empirically we find that dual solutions offer greater flexibility in navigating the tradeoff between optimization stability and estimation bias, and generally provide superior estimates in practice.
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