# Variance-sensitive Thompson sampling for generalised linear bandits, revisited

arXiv: https://arxiv.org/abs/2606.00431 · HTML: https://mlsanity.com/paper/2606.00431/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 24 references that are in the map.
- First posted on arXiv 29 May 2026.

## Builds on (most cited first, 10 of 10)

- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Parallel and Distributed Thompson Sampling for Large-scale Accelerated Exploration of Chemical Space](https://mlsanity.com/paper/1706.01825/) (2017)
- [Randomized Exploration in Generalized Linear Bandits](https://mlsanity.com/paper/1906.08947/) (2019)
- [Jointly Efficient and Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2201.01985/) (2022)
- [Self-Concordant Analysis of Generalized Linear Bandits with Forgetting](https://mlsanity.com/paper/2011.00819/) (2020)
- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update](https://mlsanity.com/paper/2507.11847/) (2025)
- [Exploration via linearly perturbed loss minimisation](https://mlsanity.com/paper/2311.07565/) (2023)
- [When and why randomised exploration works (in linear bandits)](https://mlsanity.com/paper/2502.08870/) (2025)

## Abstract (arXiv)

We prove a variance-sensitive regret bound for Thompson sampling in stochastic generalised linear bandits. The argument assumes a warm-up, after which the regret is controlled through using the Gaussian Poincar'e inequality. This bypasses the point at which previous optimism-based analyses break down. Removing the warm-up while retaining the same variance-sensitive scaling remains open, and appears nontrivial.