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We consider off-policy evaluation (OPE) in Partially Observable MarkovDecision Processes (POMDPs), where the evaluation policy depends only onobservable variables and the behavior policy depends on unobservable latentvariables. Existing works either assume no unmeasured confounders, or focus onsettings where both the observation and the state spaces are tabular. In thiswork, we first propose novel identification methods for OPE in POMDPs withlatent confounders, by introducing bridge functions that link the targetpolicy's value and the observed data distribution. We next propose minimaxestimation methods for learning these bridge functions, and construct threeestimators based on these estimated bridge functions, corresponding to a valuefunction-based estimator, a marginalized importance sampling estimator, and adoubly-robust estimator. Our proposal permits general function approximationand is thus applicable to settings with continuous or large observation/statespaces. The nonasymptotic and asymptotic properties of the proposed estimatorsare investigated in detail.

A Minimax Learning Approach to Off-Policy Evaluation in Confounded Partially Observable Markov Decision Processes