Robust Planning over Restless Groups: Engagement Interventions for a Large-Scale Maternal Telehealth Program

Abstract

In 2020, maternal mortality in India was estimated to be as high as 130 deaths per 100K live births, nearly twice the UN's target. To improve health outcomes, the non-profit ARMMAN sends automated voice messages to expecting and new mothers across India. However, 38% of mothers stop listening to these calls, missing critical preventative care information. To improve engagement, ARMMAN employs health workers to intervene by making service calls, but workers can only call a fraction of the 100K enrolled mothers. Partnering with ARMMAN, we model the problem of allocating limited interventions across mothers as a restless multi-armed bandit (RMAB), where the realities of large scale and model uncertainty present key new technical challenges. We address these with GROUPS, a double oracle–based algorithm for robust planning in RMABs with scalable grouped arms. Robustness over grouped arms requires several methodological advances. First, to adversarially select stochastic group dynamics, we develop a new method to optimize Whittle indices over transition probability intervals. Second, to learn group-level RMAB policy best responses to these adversarial environments, we introduce a weighted index heuristic. Third, we prove a key theoretical result that planning over grouped arms achieves the same minimax regret--optimal strategy as planning over individual arms, under a technical condition. Finally, using real-world data from ARMMAN, we show that GROUPS produces robust policies that reduce minimax regret by up to 50%, halving the number of preventable missed voice messages to connect more mothers with life-saving maternal health information.