# Fast Online Learning with Gaussian Prior-Driven Hierarchical Unimodal Thompson Sampling

arXiv: https://arxiv.org/abs/2602.15972 · HTML: https://mlsanity.com/paper/2602.15972/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 30 references that are in the map.
- First posted on arXiv 17 Feb 2026.

## Builds on (most cited first, 9 of 9)

- [Unimodal Bandits: Regret Lower Bounds and Optimal Algorithms](https://mlsanity.com/paper/1405.5096/) (2014)
- [Thompson Sampling Algorithms for Mean-Variance Bandits](https://mlsanity.com/paper/2002.00232/) (2020)
- [Solving Bernoulli Rank-One Bandits with Unimodal Thompson Sampling](https://mlsanity.com/paper/1912.03074/) (2019)
- [Optimal Clustering with Bandit Feedback](https://mlsanity.com/paper/2202.04294/) (2022)
- [Optimal Exploitation of Clustering and History Information in Multi-Armed Bandit](https://mlsanity.com/paper/1906.03979/) (2019)
- [Multi-Armed Bandits with Dependent Arms](https://mlsanity.com/paper/2010.09478/) (2020)
- [A Unifying Theory of Thompson Sampling for Continuous Risk-Averse Bandits](https://mlsanity.com/paper/2108.11345/) (2021)
- [Unimodal Thompson Sampling for Graph-Structured Arms](https://mlsanity.com/paper/1611.05724/) (2016)
- [Categorized Bandits](https://mlsanity.com/paper/2005.01656/) (2020)

## Abstract (arXiv)

We study a type of Multi-Armed Bandit (MAB) problems in which arms with a Gaussian reward feedback are clustered. Such an arm setting finds applications in many real-world problems, for example, mmWave communications and portfolio management with risky assets, as a result of the universality of the Gaussian distribution. Based on the Thompson Sampling algorithm with Gaussian prior (TSG) algorithm for the selection of the optimal arm, we propose our Thompson Sampling with Clustered arms under Gaussian prior (TSCG) specific to the 2-level hierarchical structure. We prove that by utilizing the 2-level structure, we can achieve a lower regret bound than we do with ordinary TSG. In addition, when the reward is Unimodal, we can reach an even lower bound on the regret by our Unimodal Thompson Sampling algorithm with Clustered Arms under Gaussian prior (UTSCG). Each of our proposed algorithms are accompanied by theoretical evaluation of the upper regret bound, and our numerical experiments confirm the advantage of our proposed algorithms.