# Neural Logistic Bandits

arXiv: https://arxiv.org/abs/2505.02069 · HTML: https://mlsanity.com/paper/2505.02069/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 27 of its 38 references that are in the map.
- First posted on arXiv 4 May 2025.

## Builds on (most cited first, 27 of 27)

- [Neural Tangent Kernel: Convergence and Generalization in Neural Networks](https://mlsanity.com/paper/1806.07572/) (2018)
- [Nearly Minimax Optimal Reinforcement Learning for Linear Mixture Markov Decision Processes](https://mlsanity.com/paper/2012.08507/) (2020)
- [Finite-Time Analysis of Kernelised Contextual Bandits](https://mlsanity.com/paper/1309.6869/) (2013)
- [Deep Bayesian Bandits Showdown: An Empirical Comparison of Bayesian Deep Networks for Thompson Sampling](https://mlsanity.com/paper/1802.09127/) (2018)
- [Neural Thompson Sampling](https://mlsanity.com/paper/2010.00827/) (2020)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Open Bandit Dataset and Pipeline: Towards Realistic and Reproducible Off-Policy Evaluation](https://mlsanity.com/paper/2008.07146/) (2020)
- [Neural Contextual Bandits with Deep Representation and Shallow Exploration](https://mlsanity.com/paper/2012.01780/) (2020)
- [Randomized Exploration in Generalized Linear Bandits](https://mlsanity.com/paper/1906.08947/) (2019)
- [Instance-Wise Minimax-Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2010.12642/) (2020)
- [EE-Net: Exploitation-Exploration Neural Networks in Contextual Bandits](https://mlsanity.com/paper/2110.03177/) (2021)
- [Improved Regret Analysis for Variance-Adaptive Linear Bandits and Horizon-Free Linear Mixture MDPs](https://mlsanity.com/paper/2111.03289/) (2021)
- [Nearly Minimax Optimal Reinforcement Learning for Discounted MDPs](https://mlsanity.com/paper/2010.00587/) (2020)
- [Jointly Efficient and Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2201.01985/) (2022)
- [Neural Contextual Bandits without Regret](https://mlsanity.com/paper/2107.03144/) (2021)
- [On the Performance of Thompson Sampling on Logistic Bandits](https://mlsanity.com/paper/1905.04654/) (2019)
- [Improved Confidence Bounds for the Linear Logistic Model and Applications to Linear Bandits](https://mlsanity.com/paper/2011.11222/) (2020)
- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Improved Regret Bounds of (Multinomial) Logistic Bandits via Regret-to-Confidence-Set Conversion](https://mlsanity.com/paper/2310.18554/) (2023)
- [Generalized Linear Bandits with Limited Adaptivity](https://mlsanity.com/paper/2404.06831/) (2024)
- [Nearly Minimax Optimal Regret for Multinomial Logistic Bandit](https://mlsanity.com/paper/2405.09831/) (2024)
- [Deep Neural Linear Bandits: Overcoming Catastrophic Forgetting through Likelihood Matching](https://mlsanity.com/paper/1901.08612/) (2019)
- [Learning Neural Contextual Bandits Through Perturbed Rewards](https://mlsanity.com/paper/2201.09910/) (2022)
- [Improved Online Confidence Bounds for Multinomial Logistic Bandits](https://mlsanity.com/paper/2502.10020/) (2025)
- [Double Doubly Robust Thompson Sampling for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/2209.06983/) (2022)
- [Norm-Agnostic Linear Bandits](https://mlsanity.com/paper/2205.01257/) (2022)
- [Neural Dueling Bandits: Preference-Based Optimization with Human Feedback](https://mlsanity.com/paper/2407.17112/) (2024)

## Built on by (most cited first, 6 of 6)

- [Generalized Kernelized Bandits: A Novel Self-Normalized Bernstein-Like Dimension-Free Inequality and Regret Bounds](https://mlsanity.com/paper/2508.01681/) (2025)
- [Queue Length Regret Bounds for Contextual Queueing Bandits](https://mlsanity.com/paper/2601.19300/) (2026)
- [Algorithm for Contextual Queueing Bandits with Rate-Optimal Queue Length Regret](https://mlsanity.com/paper/2606.09668/) (2026)
- [Logistic Bandits with tildeO(√dT) Regret without Context Diversity Assumptions](https://mlsanity.com/paper/2604.22161/) (2026)
- [CASCADE: Case-Based Continual Adaptation for Large Language Models During Deployment](https://mlsanity.com/paper/2605.06702/) (2026)
- [Minimax Optimal Regret for Causal Logistic Bandits with Counterfactual Fairness](https://mlsanity.com/paper/2610.01377/) (2026)

## Abstract (arXiv)

We study the problem of neural logistic bandits, where the main task is to learn an unknown reward function within a logistic link function using a neural network. Existing approaches either exhibit unfavorable dependencies on kappa, where 1/kappa represents the minimum variance of reward distributions, or suffer from direct dependence on the feature dimension d, which can be huge in neural network-based settings. In this work, we introduce a novel Bernstein-type inequality for self-normalized vector-valued martingales that is designed to bypass a direct dependence on the ambient dimension. This lets us deduce a regret upper bound that grows with the effective dimension widetilded, not the feature dimension, while keeping a minimal dependence on kappa. Based on the concentration inequality, we propose two algorithms, NeuralLog-UCB-1 and NeuralLog-UCB-2, that guarantee regret upper bounds of order widetildeO(widetilded√kappa T) and widetildeO(widetilded√T/kappa), respectively, improving on the existing results. Lastly, we report numerical results on both synthetic and real datasets to validate our theoretical findings.