dorsal/arxiv
View SchemaA belief-state restless bandit model for treatment adherence: Whittle indexability via partial conservation laws
| Authors | José Niño-Mora, Ángel Pellitero García |
|---|---|
| Categories | |
| ArXiv ID | 2601.06976vv1 |
| URL | https://arxiv.org/abs/2601.06976 |
| License | http://arxiv.org/licenses/nonexclusive-distrib/1.0/ |
Abstract
We study capacity-constrained treatment-adherence outreach via a belief-state restless multi-armed bandit model where patients are a partially observed two-state (adherent/nonadherent) Markov processes and interventions induce reset-type belief dynamics. Using partial conservation laws (PCLs), we establish Whittle indexability of the single-patient problem and derive a closed-form Whittle (marginal productivity) index, together with closed-form reward/work performance metrics under threshold policies and an explicit optimal threshold map. This yields an analytic Lagrangian relaxation: the single-patient Lagrangian value is a piecewise-affine convex function of the intervention price, enabling efficient computation of multi-patient dual bounds and certified relative optimality gaps. We also analyze how the Whittle index depends on the lapse and spontaneous-recovery parameters, providing qualitative insights on intervention priorities. In a large-scale numerical study over heterogeneous two-type populations, we compare Whittle's index policy with a myopic index rule and simple baselines; while myopic is highly competitive on most instances, Whittle's policy yields substantial gains in tight-capacity regimes with a fragile minority, reaching up to about $26\%$ higher reward and markedly smaller relative optimality gaps.
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"abstract": "We study capacity-constrained treatment-adherence outreach via a belief-state restless multi-armed bandit model where patients are a partially observed two-state (adherent/nonadherent) Markov processes and interventions induce reset-type belief dynamics. Using partial conservation laws (PCLs), we establish Whittle indexability of the single-patient problem and derive a closed-form Whittle (marginal productivity) index, together with closed-form reward/work performance metrics under threshold policies and an explicit optimal threshold map. This yields an analytic Lagrangian relaxation: the single-patient Lagrangian value is a piecewise-affine convex function of the intervention price, enabling efficient computation of multi-patient dual bounds and certified relative optimality gaps. We also analyze how the Whittle index depends on the lapse and spontaneous-recovery parameters, providing qualitative insights on intervention priorities. In a large-scale numerical study over heterogeneous two-type populations, we compare Whittle\u0027s index policy with a myopic index rule and simple baselines; while myopic is highly competitive on most instances, Whittle\u0027s policy yields substantial gains in tight-capacity regimes with a fragile minority, reaching up to about $26\\%$ higher reward and markedly smaller relative optimality gaps.",
"arxiv_id": "2601.06976",
"authors": [
"Jos\u00e9 Ni\u00f1o-Mora",
"\u00c1ngel Pellitero Garc\u00eda"
],
"categories": [
"math.OC"
],
"license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
"title": "A belief-state restless bandit model for treatment adherence: Whittle indexability via partial conservation laws",
"url": "https://arxiv.org/abs/2601.06976",
"version": "v1"
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