Collapsing Bandits and Their Application to Public Health Interventions
This work addresses the challenge of optimizing public health interventions, such as patient monitoring for tuberculosis medication adherence, by providing a scalable solution for healthcare workers to maximize patient health outcomes.
The paper tackles the problem of managing a limited budget of interventions in restless multi-armed bandits with a collapsing structure, where playing an arm fully reveals its state, and achieves a 3-order-of-magnitude speedup in algorithm runtime while maintaining similar performance to state-of-the-art methods.
We propose and study Collpasing Bandits, a new restless multi-armed bandit (RMAB) setting in which each arm follows a binary-state Markovian process with a special structure: when an arm is played, the state is fully observed, thus "collapsing" any uncertainty, but when an arm is passive, no observation is made, thus allowing uncertainty to evolve. The goal is to keep as many arms in the "good" state as possible by planning a limited budget of actions per round. Such Collapsing Bandits are natural models for many healthcare domains in which workers must simultaneously monitor patients and deliver interventions in a way that maximizes the health of their patient cohort. Our main contributions are as follows: (i) Building on the Whittle index technique for RMABs, we derive conditions under which the Collapsing Bandits problem is indexable. Our derivation hinges on novel conditions that characterize when the optimal policies may take the form of either "forward" or "reverse" threshold policies. (ii) We exploit the optimality of threshold policies to build fast algorithms for computing the Whittle index, including a closed-form. (iii) We evaluate our algorithm on several data distributions including data from a real-world healthcare task in which a worker must monitor and deliver interventions to maximize their patients' adherence to tuberculosis medication. Our algorithm achieves a 3-order-of-magnitude speedup compared to state-of-the-art RMAB techniques while achieving similar performance.