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We propose and study Collpasing Bandits, a new restless multi-armed bandit(RMAB) setting in which each arm follows a binary-state Markovian process witha special structure: when an arm is played, the state is fully observed, thus"collapsing" any uncertainty, but when an arm is passive, no observation ismade, thus allowing uncertainty to evolve. The goal is to keep as many arms inthe "good" state as possible by planning a limited budget of actions per round.Such Collapsing Bandits are natural models for many healthcare domains in whichworkers must simultaneously monitor patients and deliver interventions in a waythat maximizes the health of their patient cohort. Our main contributions areas follows: (i) Building on the Whittle index technique for RMABs, we deriveconditions under which the Collapsing Bandits problem is indexable. Ourderivation hinges on novel conditions that characterize when the optimalpolicies may take the form of either "forward" or "reverse" threshold policies.(ii) We exploit the optimality of threshold policies to build fast algorithmsfor computing the Whittle index, including a closed-form. (iii) We evaluate ouralgorithm on several data distributions including data from a real-worldhealthcare task in which a worker must monitor and deliver interventions tomaximize their patients' adherence to tuberculosis medication. Our algorithmachieves a 3-order-of-magnitude speedup compared to state-of-the-art RMABtechniques while achieving similar performance.

Collapsing Bandits and Their Application to Public Health Interventions