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From Relaxed Indexability to Exact Indexability: A $t$-Step Approach for Partially Observable Restless Bandits

arXiv · AI, language, vision and robotics · article · Aug 25, 2026 · UTC

Whittle index policies offer a scalable method for restless multi-armed bandits, but under partial observability even determining the indifference subsidy at a single belief requires solving an infinite-horizon belief-state problem with no closed-form value function. Liu [10] addresses this difficulty by linearizing the unknown decision boundary, leading to a linear system and a closed-form approximate Whittle index. However, the resulting threshold uses only a one-step active--passive comparison and does not account for longer-horizon continuation values. We extend this framework to a \emph{$

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