# Near Optimal Pure Exploration in Logistic Bandits

arXiv: https://arxiv.org/abs/2410.20640 · HTML: https://mlsanity.com/paper/2410.20640/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 26 references that are in the map.
- First posted on arXiv 28 Oct 2024.

## Builds on (most cited first, 12 of 12)

- [Optimal Best Arm Identification with Fixed Confidence](https://mlsanity.com/paper/1602.04589/) (2016)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Best-Arm Identification in Linear Bandits](https://mlsanity.com/paper/1409.6110/) (2014)
- [Sequential Experimental Design for Transductive Linear Bandits](https://mlsanity.com/paper/1906.08399/) (2019)
- [Optimal Best-arm Identification in Linear Bandits](https://mlsanity.com/paper/2006.16073/) (2020)
- [Gamification of Pure Exploration for Linear Bandits](https://mlsanity.com/paper/2007.00953/) (2020)
- [An optimal algorithm for the Thresholding Bandit Problem](https://mlsanity.com/paper/1605.08671/) (2016)
- [Jointly Efficient and Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2201.01985/) (2022)
- [Improved Confidence Bounds for the Linear Logistic Model and Applications to Linear Bandits](https://mlsanity.com/paper/2011.11222/) (2020)
- [Good Arm Identification via Bandit Feedback](https://mlsanity.com/paper/1710.06360/) (2017)
- [Self-Concordant Analysis of Generalized Linear Bandits with Forgetting](https://mlsanity.com/paper/2011.00819/) (2020)
- [Best Arm Identification in Generalized Linear Bandits](https://mlsanity.com/paper/1905.08224/) (2019)

## Built on by (most cited first, 2 of 2)

- [Best Arm Identification in Generalized Linear Bandits via Hybrid Feedback](https://mlsanity.com/paper/2605.05745/) (2026)
- [Almost Asymptotically Optimal Active Clustering Through Pairwise Observations](https://mlsanity.com/paper/2602.05690/) (2026)

## Abstract (arXiv)

Bandit algorithms have garnered significant attention due to their practical applications in real-world scenarios. However, beyond simple settings such as multi-arm or linear bandits, optimal algorithms remain scarce. Notably, no optimal solution exists for pure exploration problems in the context of generalized linear model (GLM) bandits. In this paper, we narrow this gap and develop the first track-and-stop algorithm for general pure exploration problems under the logistic bandit called logistic track-and-stop (Log-TS). Log-TS is an efficient algorithm that asymptotically matches an approximation for the instance-specific lower bound of the expected sample complexity up to a logarithmic factor.