Confounding-Robust Policy Evaluation in Infinite-Horizon Reinforcement Learning
This addresses the challenge of robust policy evaluation in batch reinforcement learning for applications like education and healthcare, where confounding is common, though it is an incremental improvement over existing sensitivity analysis methods.
The paper tackles the problem of evaluating sequential decision policies from observational data when unobserved confounding variables make exact evaluation impossible, by developing a method to estimate sharp bounds on policy values under a sensitivity model and proving convergence to these bounds with more data.
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, unobserved variables confound observed actions, 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 consider stationary or baseline unobserved confounding and compute bounds by optimizing over the set of all stationary state-occupancy ratios that agree with a new partially identified estimating equation and the sensitivity model. We prove convergence to the sharp bounds as we collect more confounded data. Although checking set membership is a linear program, the support function is given by a difficult nonconvex optimization problem. We develop approximations based on nonconvex projected gradient descent and demonstrate the resulting bounds empirically.