L\'evy bandits under Poissonian decision times

TL;DR

This paper analyzes a continuous-time multi-armed bandit problem with Poisson decision times, deriving explicit Gittins index expressions for spectrally one-sided Lévy processes and demonstrating convergence to classical Lévy bandit results.

Contribution

It provides explicit Gittins index formulas for Lévy bandits with Poisson decision times and establishes their convergence to classical models.

Findings

Explicit Gittins index in terms of scale functions

Convergence to classical Lévy bandit results

Applicable to spectrally one-sided Lévy processes

Abstract

We consider a version of the continuous-time multi-armed bandit problem where decision opportunities arrive at Poisson arrival times, and study its Gittins index policy. When driven by spectrally one-sided L\'evy processes, the Gittins index can be written explicitly in terms of the scale function, and is shown to converge to that in the classical L\'evy bandit of Kaspi and Mandelbaum (1995).