Transportable Offline Reinforcement Learning in Presence of Unmeasured Confounding

Offline reinforcement learning seeks to learn decision policies from previously collected data, but deployment environments may differ from the domains in which the data were collected, and logged variables may omit confounders that affected both historical actions and outcomes. We study offline policy learning under the joint challenges of domain discrepancy and unmeasured confounding, where multiple heterogeneous source datasets provide complementary information about a target domain. We develop a causally adjusted transportability framework combining transportability theory with instrumental variables, negative controls, and proxies to identify target-domain causal quantities. For confounded contextual bandits, identification reduces to systems of bridge-function integral equations, enabling minimax estimation from finite samples. Confidence sets for the identified quantities are then used for pessimistic policy optimization, yielding CAT-CCB. We extend the framework to episodic confounded Markov decision processes, where complementary sources identify target reward and transition mechanisms under structural and completeness conditions. Under Gaussian dynamics and linear function approximation, this yields CAT-CMDP. We establish high-probability finite-sample suboptimality guarantees that quantify the effects of approximation, estimation, source-to-target shift, offline coverage, and sample size. For bounded finite-dimensional linear classes, the contextual-bandit guarantee recovers the standard $\widetilde{\mathcal O}(N^{-1/2})$ rate. Numerical experiments support the effectiveness of the framework for learning target-domain policies from heterogeneous confounded data. Together, the results provide a principled approach when no single source dataset suffices for causal identification and policy optimization.