Reinforcement Learning for Target Zone Blood Glucose Control

Managing physiological variables within clinically safe target zones is a central challenge in healthcare, particularly for chronic conditions such as Type 1 Diabetes Mellitus (T1DM). Reinforcement learning (RL) offers promise for personalising treatment, but struggles with the delayed and heterogeneous effects of interventions. We propose a novel RL framework to study and support decision-making in T1DM technologies, such as automated insulin delivery. Our approach captures the complex temporal dynamics of treatment by unifying two control modalities: \textit{impulse control} for discrete, fast-acting interventions (e.g., insulin boluses), and \textit{switching control} for longer-acting treatments and regime shifts. The core of our method is a constrained Markov decision process augmented with physiological state features, enabling safe policy learning under clinical and resource constraints. The framework incorporates biologically realistic factors, including insulin decay, leading to policies that better reflect real-world therapeutic behaviour. While not intended for clinical deployment, this work establishes a foundation for future safe and temporally-aware RL in healthcare. We provide theoretical guarantees of convergence and demonstrate empirical improvements in a stylised T1DM control task, reducing blood glucose level violations from 22.4\% (state-of-the-art) to as low as 10.8\%.

High-Order Deep Meta-Learning with Category-Theoretic Interpretation

We introduce a new hierarchical deep learning framework for recursive higher-order meta-learning that enables neural networks (NNs) to construct, solve, and generalise across hierarchies of tasks. Central to this approach is a generative mechanism that creates \emph{virtual tasks} -- synthetic problem instances designed to enable the meta-learner to learn \emph{soft constraints} and unknown generalisable rules across related tasks. Crucially, this enables the framework to generate its own informative, task-grounded datasets thereby freeing machine learning (ML) training from the limitations of relying entirely on human-generated data. By actively exploring the virtual point landscape and seeking out tasks lower-level learners find difficult, the meta-learner iteratively refines constraint regions. This enhances inductive biases, regularises the adaptation process, and produces novel, unanticipated tasks and constraints required for generalisation. Each meta-level of the hierarchy corresponds to a progressively abstracted generalisation of problems solved at lower levels, enabling a structured and interpretable learning progression. By interpreting meta-learners as category-theoretic \emph{functors} that generate and condition a hierarchy of subordinate learners, we establish a compositional structure that supports abstraction and knowledge transfer across progressively generalised tasks. The category-theoretic perspective unifies existing meta-learning models and reveals how learning processes can be transformed and compared through functorial relationships, while offering practical design principles for structuring meta-learning. We speculate this architecture may underpin the next generation of NNs capable of autonomously generating novel, instructive tasks and their solutions, thereby advancing ML towards general artificial intelligence.