# Conditions for indexability of restless bandits and an O(K^3) algorithm to compute Whittle index

arXiv: https://arxiv.org/abs/2008.06111 · HTML: https://mlsanity.com/paper/2008.06111/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Aug 2020.

## Built on by (most cited first, 1 of 1)

- [Whittle Index Learning Algorithms for Restless Bandits with Constant Stepsizes](https://mlsanity.com/paper/2409.04605/) (2024)

## Abstract (arXiv)

Restless bandits are a class of sequential resource allocation problems concerned with allocating one or more resources among several alternative processes where the evolution of the process depends on the resource allocated to them. Such models capture the fundamental trade-offs between exploration and exploitation. In 1988, Whittle developed an index heuristic for restless bandit problems which has emerged as a popular solution approach due to its simplicity and strong empirical performance. The Whittle index heuristic is applicable if the model satisfies a technical condition known as indexability. In this paper, we present two general sufficient conditions for indexability and identify simpler to verify refinements of these conditions. We then revisit a previously proposed algorithm called adaptive greedy algorithm which is known to compute the Whittle index for a subclass of restless bandits. We show that a generalization of the adaptive greedy algorithm computes the Whittle index for all indexable restless bandits. We present an efficient implementation of this algorithm which can compute the Whittle index of a restless bandit with K states in O(K3) computations. Finally, we present a detailed numerical study which affirms the strong performance of the Whittle index heuristic.