Markovian restless bandits and index policies: A review

TL;DR

This review paper comprehensively surveys the extensive literature on Markovian restless bandits and index policies, emphasizing theoretical, algorithmic, and application aspects to stimulate future research.

Contribution

It provides a broad organized overview of the field, focusing on priority-index policies and their properties, and discusses diverse applications and recent developments.

Findings

Extensive literature on restless bandits is organized thematically.

Priority-index policies are highlighted for their tractability and empirical success.

The paper identifies gaps and future directions for research.

Abstract

The restless multi-armed bandit problem is a paradigmatic modeling framework for optimal dynamic priority allocation in stochastic models of wide-ranging applications that has been widely investigated and applied since its inception in a seminal paper by Whittle in the late 1980s. The problem has generated a vast and fast-growing literature from which a significant sample is thematically organized and reviewed in this paper. While the main focus is on priority-index policies due to their intuitive appeal, tractability, asymptotic optimality properties, and often strong empirical performance, other lines of work are also reviewed. Theoretical and algorithmic developments are discussed, along with diverse applications. The main goals are to highlight the remarkable breadth of work that has been carried out on the topic and to stimulate further research in the field.