Abstract
Thompson Sampling provides an efficient technique to introduce prior knowledge in the multiarmed bandit problem, along with providing remarkable empirical performance. In this paper,
we revisit the Thompson Sampling algorithm under rewards drawn from symmetric ?-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 ?-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