Transportable Offline Reinforcement Learning in Presence of Unmeasured Confounding

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.

Reinforcement learning (RL) is increasingly used to train robust, adaptable systems across healthcare, e-commerce, and robotics. In these settings, legal, ethical, or logistical concerns may preclude certain key variables that drive decisions from being collected during deployment time. This gives rise to a setting known as runtime confounding: the logged data hold full observability, but deployment time lacks knowledge of certain variables, known as runtime confounders. Unlike single timepoint and non-adaptive settings, runtime confounding under reinforcement learning has the potential to propagate over time, as earlier decisions affect future states, observations, and action assignments, leading to biased learning. We address these problems with three contributions: we (1) develop policy learning algorithms under runtime-confounding, (2) develop semi-parametric efficient off-policy estimation procedures, and (3) provide diagnostics for understanding the price of runtime confounding.

Model-based reinforcement learning is attractive for sequential decision-making because it explicitly estimates reward and transition models and then supports planning through simulated rollouts. In offline settings with hidden confounding, however, models learned directly from observational data may be biased. This challenge is especially pronounced in partially observable systems, where latent factors may jointly affect actions, rewards, and future observations. Recent work has shown that policy evaluation in such confounded partially observable Markov decision processes (POMDPs) can be reduced to estimating reward-emission and observation-transition bridge functions satisfying conditional moment restrictions (CMRs). In this paper, we study the statistical estimation of these bridge functions. We formulate bridge learning as a CMR problem with nuisance objects given by a conditional mean embedding and a conditional density. We then develop a $K$-fold cross-fitted extension of the existing two-stage bridge estimator. The proposed procedure preserves the original bridge-based identification strategy while using the available data more efficiently than a single sample split. We also derive an oracle-comparator bound for the cross-fitted estimator and decompose the resulting error into a Stage I term induced by nuisance estimation and a Stage II term induced by empirical averaging.