Off-policy reinforcement learning enables near-optimal policy from suboptimal experience, thereby provisions opportunity for artificial intelligence applications in healthcare. Previous works have mainly framed patient-clinician interactions as Markov decision processes, while true physiological states are not necessarily fully observable from clinical data. We capture this situation with partially observable Markov decision process, in which an agent optimises its actions in a belief represented as a distribution of patient states inferred from individual history trajectories. A Gaussian mixture model is fitted for the observed data. Moreover, we take into account the fact that nuance in pharmaceutical dosage could presumably result in significantly different effect by modelling a continuous policy through a Gaussian approximator directly in the policy space, i.e. the actor. To address the challenge of infinite number of possible belief states which renders exact value iteration intractable, we evaluate and plan for only every encountered belief, through heuristic search tree by tightly maintaining lower and upper bounds of the true value of belief. We further resort to function approximations to update value bounds estimation, i.e. the critic, so that the tree search can be improved through more compact bounds at the fringe nodes that will be back-propagated to the root. Both actor and critic parameters are learned via gradient-based approaches. Our proposed policy trained from real intensive care unit data is capable of dictating dosing on vasopressors and intravenous fluids for sepsis patients that lead to the best patient outcomes.
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