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This paper studies restless multi-armed bandit (RMAB) problems with unknownarm transition dynamics but with known correlated arm features. The goal is tolearn a model to predict transition dynamics given features, where the Whittleindex policy solves the RMAB problems using predicted transitions. However,prior works often learn the model by maximizing the predictive accuracy insteadof final RMAB solution quality, causing a mismatch between training andevaluation objectives. To address this shortcoming, we propose a novel approachfor decision-focused learning in RMAB that directly trains the predictive modelto maximize the Whittle index solution quality. We present three keycontributions: (i) we establish differentiability of the Whittle index policyto support decision-focused learning; (ii) we significantly improve thescalability of decision-focused learning approaches in sequential problems,specifically RMAB problems; (iii) we apply our algorithm to a previouslycollected dataset of maternal and child health to demonstrate its performance.Indeed, our algorithm is the first for decision-focused learning in RMAB thatscales to real-world problem sizes.

Scalable Decision-Focused Learning in Restless Multi-Armed Bandits with Application to Maternal and Child Health