# When are Kalman-filter restless bandits indexable?

arXiv: https://arxiv.org/abs/1509.04541 · HTML: https://mlsanity.com/paper/1509.04541/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 15 Sep 2015.

## Built on by (most cited first, 4 of 4)

- [NeurWIN: Neural Whittle Index Network For Restless Bandits Via Deep RL](https://mlsanity.com/paper/2110.02128/) (2021)
- [Online Learning of Whittle Indices for Restless Bandits with Non-Stationary Transition Kernels](https://mlsanity.com/paper/2506.18186/) (2025)
- [An Index Policy Based on Sarsa and Q-learning for Heterogeneous Smart Target Tracking](https://mlsanity.com/paper/2402.12015/) (2024)
- [From Relaxed Indexability to Exact Indexability: A t-Step Approach for Partially Observable Restless Bandits](https://mlsanity.com/paper/2608.24167/) (2026)

## Abstract (arXiv)

We study the restless bandit associated with an extremely simple scalar Kalman filter model in discrete time. Under certain assumptions, we prove that the problem is indexable in the sense that the Whittle index is a non-decreasing function of the relevant belief state. In spite of the long history of this problem, this appears to be the first such proof. We use results about Schur-convexity and mechanical words, which are particular binary strings intimately related to palindromes.