Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning

Off-policy evaluation of sequential decision policies from observational data is necessary in applications of batch reinforcement learning such as education and healthcare. In such settings, however, observed actions are often confounded with transitions by unobserved variables, rendering exact evaluation of new policies impossible, i.e., unidentifiable. We develop a robust approach that estimates sharp bounds on the (unidentifiable) value of a given policy in an infinite-horizon problem given data from another policy with unobserved confounding subject to a sensitivity model. We phrase the problem precisely as computing the support function of the set of all stationary state-occupancy ratios that agree with both the data and the sensitivity model. We show how to express this set using a new partially identified estimating equation and prove convergence to the sharp bounds, as we collect more confounded data. We prove that membership in the set can be checked by solving a linear program, while the support function is given by a difficult nonconvex optimization problem. We leverage an analytical solution for the finite-state-space case to develop approximations based on nonconvex projected gradient descent. We demonstrate the resulting bounds empirically.