A belief-state restless bandit model for treatment adherence: Whittle indexability via partial conservation laws

Mathematics > Optimization and Control [Submitted on 11 Jan 2026 (v1), last revised 15 Jun 2026 (this version, v2)] Title:A belief-state restless bandit model for treatment adherence: Whittle indexability via partial conservation laws View PDF HTML (experimental)Abstract:We study clinically motivated capacity-constrained treatment-adherence outreach through a belief-state restless multi-armed bandit model, in which each patient is a partially observed two-state Markov decision process and interventions induce reset-type belief dynamics. For the discounted criterion, partial conservation law (PCL)-based conditions are used to establish single-patient threshold-policy optimality and indexability (threshold-indexability) and yield a closed-form Whittle index, threshold performance metrics, and an explicit optimal threshold map. We also prove a single-patient long-run average analogue on the invariant belief core and obtain an explicit average-criterion Whittle index. For the multi-patient model, the PCL-derived formulas give an analytic Lagrangian relaxation, efficient dual bounds, and computable Lagrangian index benchmark policies, including a forced-capacity variant. We analyze how the Whittle index depends on lapse and spontaneous-recovery probabilities. In large-scale experiments with two-type, three-type, and jittered finite-mixture populations, the Whittle and forced-capacity Lagrangian index policies are the strongest performers, while myopic prioritization can be substantially worse under tight capacity. Submission history From: José Niño-Mora [view email][v1] Sun, 11 Jan 2026 16:18:07 UTC (332 KB) [v2] Mon, 15 Jun 2026 21:30:34 UTC (325 KB) References & Citations Loading... Bibliographic and Citation Tools Bibliographic Explorer (What is the Explorer?) Connected Papers (What is Connected Papers?) Litmaps (What is Litmaps?) scite Smart Citations (What are Smart Citations?) Code, Data and Media Associated with this Article alphaXiv (What is alphaXiv?) CatalyzeX Code Finder for Papers (What is CatalyzeX?) DagsHub (What is DagsHub?) Gotit.pub (What is GotitPub?) Hugging Face (What is Huggingface?) ScienceCast (What is ScienceCast?) Demos Recommenders and Search Tools Influence Flower (What are Influence Flowers?) CORE Recommender (What is CORE?) arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.