When are Kalman-filter restless bandits indexable?
This addresses a foundational problem in stochastic control and bandit theory, providing a theoretical advance for researchers in optimization and decision-making under uncertainty.
The paper tackles the problem of proving indexability for a restless bandit with a simple scalar Kalman filter model, and under certain assumptions, it shows that the Whittle index is a non-decreasing function of the belief state, marking the first such proof.
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.