Year: 2023
Type: preprint
Abstract: We consider Thompson sampling for linear bandit problems with finitely many independent arms, where rewards are sampled from normal distributions that are linearly dependent on unknown parameter vectors and with unknown variance. Specifically, with a Bayesian formulation we consider multivariate normal-gamma priors to represent environment uncertainty for all involved parameters. We show that our chosen sampling prior is a conjugate prior to the reward model and derive a Bayesian regret bound for Thompson sampling under the condition that the 5/2-moment of the variance distribution exist.
Source: arXiv (Cornell University)
Authors: Lindenberg, Björn, Lindahl, Karl-Olof
Language: English
Field: Decision Sciences
Domain: Social Sciences
Open Access status: green
OpenAlex ID: W4323572015