# On the Performance of Thompson Sampling on Logistic Bandits

arXiv: https://arxiv.org/abs/1905.04654 · HTML: https://mlsanity.com/paper/1905.04654/

## Key facts

- Cited by 32 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 May 2019.

## Built on by (most cited first, 30 of 32)

- [Reinforcement Learning, Bit by Bit](https://mlsanity.com/paper/2103.04047/) (2021)
- [Jointly Efficient and Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2201.01985/) (2022)
- [Provable Model-based Nonlinear Bandit and Reinforcement Learning: Shelve Optimism, Embrace Virtual Curvature](https://mlsanity.com/paper/2102.04168/) (2021)
- [On the Theory of Reinforcement Learning with Once-per-Episode Feedback](https://mlsanity.com/paper/2105.14363/) (2021)
- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [An Analysis of Ensemble Sampling](https://mlsanity.com/paper/2203.01303/) (2022)
- [Langevin Monte Carlo for Contextual Bandits](https://mlsanity.com/paper/2206.11254/) (2022)
- [Information Directed Sampling for Sparse Linear Bandits](https://mlsanity.com/paper/2105.14267/) (2021)
- [Lifting the Information Ratio: An Information-Theoretic Analysis of Thompson Sampling for Contextual Bandits](https://mlsanity.com/paper/2205.13924/) (2022)
- [Improved Online Confidence Bounds for Multinomial Logistic Bandits](https://mlsanity.com/paper/2502.10020/) (2025)
- [Scalable Neural Contextual Bandit for Recommender Systems](https://mlsanity.com/paper/2306.14834/) (2023)
- [Learning to be Fair: A Consequentialist Approach to Equitable Decision-Making](https://mlsanity.com/paper/2109.08792/) (2021)
- [An Information-Theoretic Analysis of Nonstationary Bandit Learning](https://mlsanity.com/paper/2302.04452/) (2023)
- [Tight Regret Bounds for Single-pass Streaming Multi-armed Bandits](https://mlsanity.com/paper/2306.02208/) (2023)
- [An Experimental Design Approach for Regret Minimization in Logistic Bandits](https://mlsanity.com/paper/2202.02407/) (2022)
- [Neural Logistic Bandits](https://mlsanity.com/paper/2505.02069/) (2025)
- [Revisiting Weighted Strategy for Non-stationary Parametric Bandits and MDPs](https://mlsanity.com/paper/2601.01069/) (2026)
- [Apple Tasting Revisited: Bayesian Approaches to Partially Monitored Online Binary Classification](https://mlsanity.com/paper/2109.14412/) (2021)
- [On Bits and Bandits: Quantifying the Regret-Information Trade-off](https://mlsanity.com/paper/2405.16581/) (2024)
- [PromptWise: Online Learning for Cost-Aware Prompt Assignment in Generative Models](https://mlsanity.com/paper/2505.18901/) (2025)
- [Eluder dimension: localise it!](https://mlsanity.com/paper/2601.09825/) (2026)
- [Practical Bayesian Algorithm Execution via Posterior Sampling](https://mlsanity.com/paper/2410.20596/) (2024)
- [Preference-based Reinforcement Learning beyond Pairwise Comparisons: Benefits of Multiple Options](https://mlsanity.com/paper/2510.18713/) (2025)
- [Overcoming Prior Misspecification in Online Learning to Rank](https://mlsanity.com/paper/2301.10651/) (2023)
- [An Information-Theoretic Analysis of Thompson Sampling for Logistic Bandits](https://mlsanity.com/paper/2412.02861/) (2024)
- [A Jointly Efficient and Optimal Algorithm for Heteroskedastic Generalized Linear Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2602.10971/) (2026)
- [Logistic Bandits with tildeO(√dT) Regret without Context Diversity Assumptions](https://mlsanity.com/paper/2604.22161/) (2026)
- [On Learning to Rank Long Sequences with Contextual Bandits](https://mlsanity.com/paper/2106.03546/) (2021)
- [Revisiting Weighted Strategy for Non-stationary Parametric Bandits](https://mlsanity.com/paper/2303.02691/) (2023)
- [An Information-Theoretic Analysis of Thompson Sampling with Infinite Action Spaces](https://mlsanity.com/paper/2502.02140/) (2025)

## Abstract (arXiv)

We study the logistic bandit, in which rewards are binary with success probability exp(β a^top θ) / (1 + exp(β a^top θ)) and actions a and coefficients θ are within the d-dimensional unit ball. While prior regret bounds for algorithms that address the logistic bandit exhibit exponential dependence on the slope parameter β, we establish a regret bound for Thompson sampling that is independent of β. Specifically, we establish that, when the set of feasible actions is identical to the set of possible coefficient vectors, the Bayesian regret of Thompson sampling is tildeO(d√T). We also establish a tildeO(√dη T/λ) bound that applies more broadly, where λ is the worst-case optimal log-odds and η is the "fragility dimension," a new statistic we define to capture the degree to which an optimal action for one model fails to satisfice for others. We demonstrate that the fragility dimension plays an essential role by showing that, for any ε > 0, no algorithm can achieve poly(d, 1/λ)· T1-ε regret.