# Randomized Exploration in Generalized Linear Bandits

arXiv: https://arxiv.org/abs/1906.08947 · HTML: https://mlsanity.com/paper/1906.08947/

## Key facts

- Cited by 70 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 21 Jun 2019.

## Built on by (most cited first, 30 of 70)

- [Randomized Exploration for Reinforcement Learning with General Value Function Approximation](https://mlsanity.com/paper/2106.07841/) (2021)
- [Jointly Efficient and Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2201.01985/) (2022)
- [A Provably Efficient Model-Free Posterior Sampling Method for Episodic Reinforcement Learning](https://mlsanity.com/paper/2208.10904/) (2022)
- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Metadata-based Multi-Task Bandits with Bayesian Hierarchical Models](https://mlsanity.com/paper/2108.06422/) (2021)
- [Random Boxes Are Open-world Object Detectors](https://mlsanity.com/paper/2307.08249/) (2023)
- [Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion](https://mlsanity.com/paper/2310.18554/) (2023)
- [Fixed-Budget Best-Arm Identification in Structured Bandits](https://mlsanity.com/paper/2106.04763/) (2021)
- [Langevin Monte Carlo for Contextual Bandits](https://mlsanity.com/paper/2206.11254/) (2022)
- [Multinomial Logit Contextual Bandits: Provable Optimality and Practicality](https://mlsanity.com/paper/2103.13929/) (2021)
- [Nearly Minimax Optimal Regret for Multinomial Logistic Bandit](https://mlsanity.com/paper/2405.09831/) (2024)
- [Understanding the Eluder Dimension](https://mlsanity.com/paper/2104.06970/) (2021)
- [Lifting the Information Ratio: An Information-Theoretic Analysis of Thompson Sampling for Contextual Bandits](https://mlsanity.com/paper/2205.13924/) (2022)
- [Learning Neural Contextual Bandits Through Perturbed Rewards](https://mlsanity.com/paper/2201.09910/) (2022)
- [Active Learning with Safety Constraints](https://mlsanity.com/paper/2206.11183/) (2022)
- [Model-Based Reinforcement Learning with Multinomial Logistic Function Approximation](https://mlsanity.com/paper/2212.13540/) (2022)
- [Exploration via linearly perturbed loss minimisation](https://mlsanity.com/paper/2311.07565/) (2023)
- [Diffusion Approximations for Thompson Sampling in the Small Gap Regime](https://mlsanity.com/paper/2105.09232/) (2021)
- [Towards Scalable and Robust Structured Bandits: A Meta-Learning Framework](https://mlsanity.com/paper/2202.13227/) (2022)
- [Active Learning for Direct Preference Optimization](https://mlsanity.com/paper/2503.01076/) (2025)
- [Residual Bootstrap Exploration for Stochastic Linear Bandit](https://mlsanity.com/paper/2202.11474/) (2022)
- [When and why randomised exploration works (in linear bandits)](https://mlsanity.com/paper/2502.08870/) (2025)
- [Posterior Behavioral Cloning: Pretraining BC Policies for Efficient RL Finetuning](https://mlsanity.com/paper/2512.16911/) (2025)
- [Causal Bandits with General Causal Models and Interventions](https://mlsanity.com/paper/2403.00233/) (2024)
- [VITS : Variational Inference Thompson Sampling for contextual bandits](https://mlsanity.com/paper/2307.10167/) (2023)
- [Active Preference Learning for Ordering Items In- and Out-of-sample](https://mlsanity.com/paper/2405.03059/) (2024)
- [Random Latent Exploration for Deep Reinforcement Learning](https://mlsanity.com/paper/2407.13755/) (2024)
- [Improved Regret of Linear Ensemble Sampling](https://mlsanity.com/paper/2411.03932/) (2024)
- [Neural Logistic Bandits](https://mlsanity.com/paper/2505.02069/) (2025)
- [Single Index Bandits: Generalized Linear Contextual Bandits with Unknown Reward Functions](https://mlsanity.com/paper/2506.12751/) (2025)

## Abstract (arXiv)

We study two randomized algorithms for generalized linear bandits. The first, GLM-TSL, samples a generalized linear model (GLM) from the Laplace approximation to the posterior distribution. The second, GLM-FPL, fits a GLM to a randomly perturbed history of past rewards. We analyze both algorithms and derive tildeO(d √n log K) upper bounds on their n-round regret, where d is the number of features and K is the number of arms. The former improves on prior work while the latter is the first for Gaussian noise perturbations in non-linear models. We empirically evaluate both GLM-TSL and GLM-FPL in logistic bandits, and apply GLM-FPL to neural network bandits. Our work showcases the role of randomization, beyond posterior sampling, in exploration.