Type 1 diabetes is a chronic metabolic disease that requires regular insulin injections to regulate blood glucose levels. Recently, traditional manual approaches to diabetes management have been revolutionized by the use of continuous glucose monitors and insulin pumps to automate this process as much as possible. However, these approaches either require manual meal announcements, which is subject to human error, or need to be fine-tuned on a specific patient, which is challenging and risky. In this paper, we present a fully-automated patient-agnostic model that does not require any human intervention or patient-specific adjustments. Specifically, we use a deep reinforcement learning algorithm (Soft Actor-Critic) trained on an improved version of the FDA-approved UVA/Padova simulator for type 1 diabetes patients. By adding standardized meal scenarios to the simulator, we are making our results reproducible and comparable for future studies. Our model is compared to several baseline methods and evaluated on unseen patients by employing a rigorous train/validation/test split of the virtual cohort. Our patient-agnostic model achieves a score of 80.3% time in range compared to 77.3% for the patient-specific PID baseline and 72.7% for the state-of-the-art approach by Fox et al. [1]. Our approach has the potential to increase the ease and safety of using a fully-automated system for type 1 diabetes management in a real-world setting. Our code, models, and the improved simulator are available at https://github.com/Tom-Milton/RLAP.

Probabilistic context-free grammars (PCFGs) and dynamic Bayesian networks (DBNs) are widely used sequence models with complementary strengths and limitations. While PCFGs allow for nested hierarchical dependencies (tree structures), their latent variables (non-terminal symbols) have to be discrete. In contrast, DBNs allow for continuous latent variables, but the dependencies are strictly sequential (chain structure). Therefore, neither can be applied if the latent variables are assumed to be continuous and also to have a nested hierarchical dependency structure. In this paper, we present Recursive Bayesian Networks (RBNs), which generalise and unify PCFGs and DBNs, combining their strengths and containing both as special cases. RBNs define a joint distribution over tree-structured Bayesian networks with discrete or continuous latent variables. The main challenge lies in performing joint inference over the exponential number of possible structures and the continuous variables. We provide two solutions: 1) For arbitrary RBNs, we generalise inside and outside probabilities from PCFGs to the mixed discrete-continuous case, which allows for maximum posterior estimates of the continuous latent variables via gradient descent, while marginalising over network structures. 2) For Gaussian RBNs, we additionally derive an analytic approximation of the marginal data likelihood (evidence) and marginal posterior distribution, allowing for robust parameter optimisation and Bayesian inference. The capacity and diverse applications of RBNs are illustrated on two examples: In a quantitative evaluation on synthetic data, we demonstrate and discuss the advantage of RBNs for segmentation and tree induction from noisy sequences, compared to change point detection and hierarchical clustering. In an application to musical data, we approach the unsolved problem of hierarchical music analysis from the raw note level and compare our results to expert annotations.