Breaking the Order Barrier: Off-Policy Evaluation for Confounded POMDPs

We consider off-policy evaluation (OPE) in Partially Observable Markov Decision Processes (POMDPs) with unobserved confounding. Recent advances have introduced bridge-function to circumvent unmeasured confounding and develop estimators for the policy value, yet the statistical error bounds of them related to the length of horizon T and the size of the state-action space |O||A| remain largely unexplored. In this paper, we systematically investigate the finite-sample error bounds of OPE estimators in finite-horizon tabular confounded POMDPs. Specifically, we show that under certain rank conditions, the estimation error for policy value can achieve a rate of O(T1.5/ n), excluding the cardinality of the observation space |O| and the action space |A|. With an additional mild condition on the concentrability coefficients in confounded POMDPs, the rate of estimation error can be improved to O(T/ n).