# Thompson Sampling on Symmetric $\alpha$-Stable Bandits

## TL;DR

This paper extends Thompson Sampling to symmetric alpha-stable bandits, providing new algorithms with finite-time regret bounds and demonstrating superior performance in heavy-tailed reward settings common in finance and economics.

## Contribution

The paper introduces two novel Thompson Sampling algorithms for symmetric alpha-stable rewards, along with finite-time regret bounds and empirical validation.

## Key findings

- Thompson Sampling outperforms existing methods in heavy-tailed reward environments.
- The proposed algorithms achieve finite-time regret bounds.
- Empirical results show improved performance in finance-related applications.

## Abstract

Thompson Sampling provides an efficient technique to introduce prior knowledge in the multi-armed bandit problem, along with providing remarkable empirical performance. In this paper, we revisit the Thompson Sampling algorithm under rewards drawn from symmetric $\alpha$-stable distributions, which are a class of heavy-tailed probability distributions utilized in finance and economics, in problems such as modeling stock prices and human behavior. We present an efficient framework for posterior inference, which leads to two algorithms for Thompson Sampling in this setting. We prove finite-time regret bounds for both algorithms, and demonstrate through a series of experiments the stronger performance of Thompson Sampling in this setting. With our results, we provide an exposition of symmetric $\alpha$-stable distributions in sequential decision-making, and enable sequential Bayesian inference in applications from diverse fields in finance and complex systems that operate on heavy-tailed features.