# An Information-Theoretic Analysis of Thompson Sampling for Logistic Bandits

arXiv: https://arxiv.org/abs/2412.02861 · HTML: https://mlsanity.com/paper/2412.02861/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 10 of its 19 references that are in the map.
- First posted on arXiv 3 Dec 2024.

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

- [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)
- [An Information-Theoretic Analysis of Thompson Sampling](https://mlsanity.com/paper/1403.5341/) (2014)
- [Learning to Optimize via Information-Directed Sampling](https://mlsanity.com/paper/1403.5556/) (2014)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Randomized Exploration in Generalized Linear Bandits](https://mlsanity.com/paper/1906.08947/) (2019)
- [An Information-Theoretic Analysis for Thompson Sampling with Many Actions](https://mlsanity.com/paper/1805.11845/) (2018)
- [On the Performance of Thompson Sampling on Logistic Bandits](https://mlsanity.com/paper/1905.04654/) (2019)
- [Lifting the Information Ratio: An Information-Theoretic Analysis of Thompson Sampling for Contextual Bandits](https://mlsanity.com/paper/2205.13924/) (2022)
- [Optimistic Information Directed Sampling](https://mlsanity.com/paper/2402.15411/) (2024)

## Built on by (most cited first, 1 of 1)

- [Contextual Thompson Sampling via Generation of Missing Data](https://mlsanity.com/paper/2502.07064/) (2025)

## Abstract (arXiv)

We study the performance of the Thompson Sampling algorithm for logistic bandit problems. In this setting, an agent receives binary rewards with probabilities determined by a logistic function, exp(β langle a, θ rangle)/(1+exp(β langle a, θ rangle)), with slope parameter β>0, and where both the action a∈ A and parameter θ ∈ O lie within the d-dimensional unit ball. Adopting the information-theoretic framework introduced by Russo and Van Roy (2016), we analyze the information ratio, a statistic that quantifies the trade-off between the immediate regret incurred and the information gained about the optimal action. We improve upon previous results by establishing that the information ratio is bounded by tfrac92dα-2, where α is a minimax measure of the alignment between the action space A and the parameter space O, and is independent of β. Using this result, we derive a bound of order O(d/α√T log(β T/d)) on the Bayesian expected regret of Thompson Sampling incurred after T time steps. To our knowledge, this is the first regret bound for logistic bandits that depends only logarithmically on β while being independent of the number of actions. In particular, when the action space contains the parameter space, the bound on the expected regret is of order tildeO(d √T).