# Thompson Sampling for Linear Bandit Problems with Normal-Gamma Priors

arXiv: https://arxiv.org/abs/2303.03348 · HTML: https://mlsanity.com/paper/2303.03348/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 21 references that are in the map.
- First posted on arXiv 6 Mar 2023.

## Builds on (most cited first, 7 of 7)

- [Introduction to Multi-Armed Bandits](https://mlsanity.com/paper/1904.07272/) (2019)
- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Learning to Optimize via Information-Directed Sampling](https://mlsanity.com/paper/1403.5556/) (2014)
- [Thompson Sampling Algorithms for Mean-Variance Bandits](https://mlsanity.com/paper/2002.00232/) (2020)
- [Prior-free and prior-dependent regret bounds for Thompson Sampling](https://mlsanity.com/paper/1304.5758/) (2013)
- [Information Directed Sampling for Sparse Linear Bandits](https://mlsanity.com/paper/2105.14267/) (2021)

## Abstract (arXiv)

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.