Primary Submission Category: Causal Inference and Common Support Violations
Off policy evaluation without overlap through smoothness assumptions
Authors: Samir Khan, Johan Ugander, Martin Saveski,
Presenting Author: Samir Khan*
Existing methods for off-policy evaluation typically require either overlap or a well-specified model. In this work, we develop a new approach to off-policy evaluation that requires neither. Instead, we assume the conditional mean of the response is Lipschitz with respect to covariates. Under this assumption, we can reweight in the overlap region, and upper and lower bound the contribution of the non-overlap region by solving LPs derived from the Lipschitz condition. This approach gives partial identification bounds for the off-policy value that generalizes the Manski bounds obtained by assumptions on the range of the response.
More specifically, we: (1) derive a closed form solution to the LP that bounds the contribution of the non-overlap region, making our method highly interpretable and transparent; (2) prove that a bootstrap confidence interval for the value of the target policy is asymptotically valid, enabling inference; (3) consider settings in which there is weak overlap, and show on real data examples that in such a setting, we can shrink our confidence intervals by treating points with weak overlap as though they have no overlap. This last perspective is analogous to sample trimming, except that we do not require a change of estimand, since our smoothness assumptions allow us to partially identify the original estimand even after trimming.