Finite-Horizon Single-Pull Restless Bandits: An Efficient Index Policy For Scarce Resource Allocation
This work addresses the problem of scarce resource allocation for domains such as healthcare intervention programs, providing an efficient solution for scenarios where each agent can only receive at most one resource.
The authors tackled the problem of optimizing sequential resource allocation in scenarios with scarce resources, achieving a sub-linearly decaying average optimality gap of $ ilde{mathcal{O}}left( rac{1}{ρ^{1/2}} ight)$. Their proposed index policy demonstrates robust performance across various domains.
Restless multi-armed bandits (RMABs) have been highly successful in optimizing sequential resource allocation across many domains. However, in many practical settings with highly scarce resources, where each agent can only receive at most one resource, such as healthcare intervention programs, the standard RMAB framework falls short. To tackle such scenarios, we introduce Finite-Horizon Single-Pull RMABs (SPRMABs), a novel variant in which each arm can only be pulled once. This single-pull constraint introduces additional complexity, rendering many existing RMAB solutions suboptimal or ineffective. %To address this, we propose using dummy states to duplicate the system, ensuring that once an arm is activated, it transitions exclusively within the dummy states. To address this shortcoming, we propose using \textit{dummy states} that expand the system and enforce the one-pull constraint. We then design a lightweight index policy for this expanded system. For the first time, we demonstrate that our index policy achieves a sub-linearly decaying average optimality gap of $\tilde{\mathcal{O}}\left(\frac{1}{ρ^{1/2}}\right)$ for a finite number of arms, where $ρ$ is the scaling factor for each arm cluster. Extensive simulations validate the proposed method, showing robust performance across various domains compared to existing benchmarks.