# A new approach to Poissonian two-armed bandit problem

## TL;DR

This paper introduces a Bayesian method for solving a continuous-time two-armed bandit problem with Poisson processes, using current process history rather than posterior evolution, and provides recursive and PDE-based solutions.

## Contribution

It presents a novel Bayesian approach that leverages process history instead of posterior evolution, with recursive equations and PDEs for strategy and risk calculation.

## Key findings

- Developed recursive equations for Bayesian strategies
- Derived PDEs for limiting case analysis
- Enhanced understanding of process history in Bayesian bandit solutions

## Abstract

We consider a continuous time two-armed bandit problem in which incomes are described by Poissonian processes. We develop Bayesian approach with arbitrary prior distribution. We present two versions of recursive equation for determination of Bayesian piece-wise constant strategy and Bayesian risk and partial differential equation in the limiting case. Unlike the previously considered Bayesian settings our description uses current history of the process and not evolution of the posterior distribution.