Reinforcement Learning Under Runtime Confounding: Policy Learning and Off-Policy Evaluation

The paradigm of decision-making has been revolutionised by reinforcement learning and deep learning. Although this has led to significant progress in domains such as robotics, healthcare, and finance, the use of RL in practice is challenging, particularly when learning decision policies in high-stakes applications that may require guarantees. Traditional RL algorithms rely on a large number of online interactions with the environment, which is problematic in scenarios where online interactions are costly, dangerous, or infeasible. However, learning from offline datasets is hindered by the presence of hidden confounders. Such confounders can cause spurious correlations in the dataset and can mislead the agent into taking suboptimal or adversarial actions. Firstly, we address the problem of learning from offline datasets in the presence of hidden confounders. We work with instrumental variables (IVs) to identify the causal effect, which is an instance of a conditional moment restrictions (CMR) problem. Inspired by double/debiased machine learning, we derive a sample-efficient algorithm for solving CMR problems with convergence and optimality guarantees, which outperforms state-of-the-art algorithms. Secondly, we relax the conditions on the hidden confounders in the setting of (offline) imitation learning, and adapt our CMR estimator to derive an algorithm that can learn effective imitator policies with convergence rate guarantees. Finally, we consider the problem of learning high-level objectives expressed in linear temporal logic (LTL) and develop a provably optimal learning algorithm that improves sample efficiency over existing methods. Through evaluation on reinforcement learning benchmarks and synthetic and semi-synthetic datasets, we demonstrate the usefulness of the methods developed in this thesis in real-world decision making.

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.

Off-policy evaluation (OPE) methods estimate the value of a new reinforcement learning (RL) policy prior to deployment. Recent advances have shown that leveraging auxiliary datasets, such as those synthesized by generative models, can improve the accuracy of OPE methods. Unfortunately, such auxiliary datasets may also be biased, and existing methods for using data augmentation within OPE lack principled uncertainty quantification. In high stakes domains like healthcare, reliable uncertainty estimates are important for ensuring safe and informed deployment of RL policies. In this work, we propose two methods to construct valid confidence intervals for OPE with data augmentation. The first provides a confidence interval over $V^π(s)$, the policy value conditioned on an initial state $s$. To do so we introduce a new conformal prediction method suitable for Markov Decision Processes (MDPs) with continuous state spaces, extending prior work to higher-dimensional settings. Second, we consider the more common task of estimating the average policy performance over all initial states, $V^π$; we introduce a method that draws on ideas from doubly robust estimation and prediction powered inference. Across simulators spanning inventory management, robotics, healthcare, and a real healthcare dataset from MIMIC-IV, we find that our methods can effectively leverage auxiliary data and consistently produce confidence intervals that cover the ground truth policy values, unlike previously proposed methods. Our work enables a future in which OPE can provide rigorous uncertainty estimates for high-stakes domains.