Lévy bandits under Poissonian decision times

Paper: arXiv 2301.07798

Authors: José-Luis Pérez, Kazutoshi Yamazaki

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 Lévy processes, the Gittins index can be written explicitly in terms of the scale function, and is shown to converge to that in the classical Lévy bandit of Kaspi and Mandelbaum (1995).

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 2.0/10
• Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: This paper presents a strong theoretical contribution to continuous-time decision theory by solving a Poissonian multi-armed bandit problem using spectrally one-sided Lévy processes and scale functions. However, it is entirely theoretical with no empirical backtesting or real-world financial data applications.

Research Flowchart

  flowchart TD
    A[Research Goal: Analyze continuous-time MAB <br>with Poissonian decision times] --> B[Inputs: Spectrally one-sided Lévy processes <br>& Poisson arrival times]
    B --> C[Methodology: Formulate dynamic programming <br>& Gittins index framework]
    C --> D[Compute Gittins Index using <br>Lévy scale functions]
    D --> E[Analyze asymptotic behavior <br>as Poisson rate approaches infinity]
    E --> F[Outcomes: Explicit Gittins index formula & <br>convergence to Kaspi & Mandelbaum model]