Convex Regularization and Convergence of Policy Gradient Flows under Safety Constraints

This paper studies reinforcement learning (RL) in infinite-horizon dynamic decision processes with almost-sure safety constraints. Such safety-constrained decision processes are central to applications in autonomous systems, finance, and resource management, where policies must satisfy strict, state-dependent constraints. We consider a doubly-regularized RL framework that combines reward and parameter regularization to address these constraints within continuous state-action spaces. Specifically, we formulate the problem as a convex regularized objective with parametrized policies in the mean-field regime. Our approach leverages recent developments in mean-field theory and Wasserstein gradient flows to model policies as elements of an infinite-dimensional statistical manifold, with policy updates evolving via gradient flows on the space of parameter distributions. Our main contributions include establishing solvability conditions for safety-constrained problems, defining smooth and bounded approximations that facilitate gradient flows, and demonstrating exponential convergence towards global solutions under sufficient regularization. We provide general conditions on regularization functions, encompassing standard entropy regularization as a special case. The results also enable a particle method implementation for practical RL applications. The theoretical insights and convergence guarantees presented here offer a robust framework for safe RL in complex, high-dimensional decision-making problems.

Predicting Visit Cost of Obstructive Sleep Apnea using Electronic Healthcare Records with Transformer

Background: Obstructive sleep apnea (OSA) is growing increasingly prevalent in many countries as obesity rises. Sufficient, effective treatment of OSA entails high social and financial costs for healthcare. Objective: For treatment purposes, predicting OSA patients' visit expenses for the coming year is crucial. Reliable estimates enable healthcare decision-makers to perform careful fiscal management and budget well for effective distribution of resources to hospitals. The challenges created by scarcity of high-quality patient data are exacerbated by the fact that just a third of those data from OSA patients can be used to train analytics models: only OSA patients with more than 365 days of follow-up are relevant for predicting a year's expenditures. Methods and procedures: The authors propose a method applying two Transformer models, one for augmenting the input via data from shorter visit histories and the other predicting the costs by considering both the material thus enriched and cases with more than a year's follow-up. Results: The two-model solution permits putting the limited body of OSA patient data to productive use. Relative to a single-Transformer solution using only a third of the high-quality patient data, the solution with two models improved the prediction performance's $R^{2}$ from 88.8% to 97.5%. Even using baseline models with the model-augmented data improved the $R^{2}$ considerably, from 61.6% to 81.9%. Conclusion: The proposed method makes prediction with the most of the available high-quality data by carefully exploiting details, which are not directly relevant for answering the question of the next year's likely expenditure.