Physics-Informed Koopman-Constrained Implicit Q-Learning for Safe Offline Reinforcement Learning in Mechanical Ventilation

Mechanical ventilation management in intensive care units requires continuous optimization of ventilator parameters while adhering to clinical safety constraints. This paper presents Physics-Informed Koopman-constrained Implicit Q-Learning (PIK-IQL), a novel offline reinforcement learning framework that integrates respiratory mechanics with data-driven policy optimization. The proposed approach addresses three fundamental challenges: learning from retrospective clinical data without online interaction, incorporating physical laws governing respiratory dynamics, and ensuring policy robustness against unmeasured confounding. We develop a Physics-Informed Koopman world model that lifts nonlinear respiratory dynamics into a linear representation while preserving mechanical constraints, enabling interpretable long-horizon predictions. The Koopman-constrained IQL policy learns conservative ventilation strategies from offline trajectories using expectile regression, with hierarchical action regularization to prevent aggressive parameter adjustments. Experiments on the MIMIC-IV database (15,446 patients, 1.58 million hourly observations) demonstrate that PIK-IQL achieves a policy value improvement of 0.088 (95% CI: [0.078, 0.096]) over behavior policy, with zero aggressive actions exceeding safety thresholds. Rosenbaum sensitivity analysis confirms high causal robustness with critical Γ * = 3.0, indicating conclusions remain valid even under substantial unmeasured confounding.