---
title: "Thompson Sampling for Bandits with Clustered Arms"
authors:
  - "Emil Carlsson"
  - "Devdatt Dubhashi"
  - "Fredrik D. Johansson"
doi: "10.24963/ijcai.2021/305"
url: "https://ijcai.org/proceedings/2021/305"
pdf: "https://ijcai.org/proceedings/2021/0305.pdf"
venue: "Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence"
year: 2021
pages: "2212-2218"
track: "Main Track"
keywords:
  - "Machine Learning: Learning Theory"
  - "Machine Learning: Online Learning"
  - "Machine Learning: Reinforcement Learning"
---

# Thompson Sampling for Bandits with Clustered Arms

Emil Carlsson, Devdatt Dubhashi, Fredrik D. Johansson

*Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence*, pages 2212-2218. DOI: [10.24963/ijcai.2021/305](https://doi.org/10.24963/ijcai.2021/305)

## Abstract

We propose algorithms based on a multi-level Thompson sampling scheme, for the stochastic multi-armed bandit and its contextual variant with linear expected rewards, in the setting where arms are clustered. We show, both theoretically and empirically, how exploiting a given cluster structure can significantly improve the regret and computational cost compared to using standard Thompson sampling. In the case of the stochastic multi-armed bandit we give upper bounds on the expected cumulative regret showing how it depends on the quality of the clustering.  Finally, we perform an empirical evaluation showing that our algorithms perform well compared to previously proposed algorithms for bandits with clustered arms.