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When observed decisions depend only on observed features, off-policy policyevaluation (OPE) methods for sequential decision making problems can estimatethe performance of evaluation policies before deploying them. This assumptionis frequently violated due to unobserved confounders, unrecorded variables thatimpact both the decisions and their outcomes. We assess robustness of OPEmethods under unobserved confounding by developing worst-case bounds on theperformance of an evaluation policy. When unobserved confounders can affectevery decision in an episode, we demonstrate that even small amounts ofper-decision confounding can heavily bias OPE methods. Fortunately, in a numberof important settings found in healthcare, policy-making, operations, andtechnology, unobserved confounders may primarily affect only one of the manydecisions made. Under this less pessimistic model of one-decision confounding,we propose an efficient loss-minimization-based procedure for computingworst-case bounds, and prove its statistical consistency. On two simulatedhealthcare examples---management of sepsis patients and developmentalinterventions for autistic children---where this is a reasonable model ofconfounding, we demonstrate that our method invalidates non-robust results andprovides meaningful certificates of robustness, allowing reliable selection ofpolicies even under unobserved confounding.

Off-policy Policy Evaluation For Sequential Decisions Under Unobserved Confounding