# An Experimental Design Approach for Regret Minimization in Logistic Bandits

arXiv: https://arxiv.org/abs/2202.02407 · HTML: https://mlsanity.com/paper/2202.02407/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 42 references that are in the map.
- First posted on arXiv 4 Feb 2022.

## Builds on (most cited first, 13 of 13)

- [Beyond UCB: Optimal and Efficient Contextual Bandits with Regression Oracles](https://mlsanity.com/paper/2002.04926/) (2020)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Sequential Experimental Design for Transductive Linear Bandits](https://mlsanity.com/paper/1906.08399/) (2019)
- [Instance-Wise Minimax-Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2010.12642/) (2020)
- [High-Dimensional Experimental Design and Kernel Bandits](https://mlsanity.com/paper/2105.05806/) (2021)
- [Provably Optimal Algorithms for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/1703.00048/) (2017)
- [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)
- [Stochastic Low-Rank Bandits](https://mlsanity.com/paper/1712.04644/) (2017)
- [PG-TS: Improved Thompson Sampling for Logistic Contextual Bandits](https://mlsanity.com/paper/1805.07458/) (2018)
- [Contextual Multi-Armed Bandits for Causal Marketing](https://mlsanity.com/paper/1810.01859/) (2018)
- [Experimental Design for Regret Minimization in Linear Bandits](https://mlsanity.com/paper/2011.00576/) (2020)
- [Adaptive, Personalized Diversity for Visual Discovery](https://mlsanity.com/paper/1810.01477/) (2018)

## Built on by (most cited first, 7 of 7)

- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Generalized Linear Bandits with Limited Adaptivity](https://mlsanity.com/paper/2404.06831/) (2024)
- [Optimal Design for Human Preference Elicitation](https://mlsanity.com/paper/2404.13895/) (2024)
- [Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update](https://mlsanity.com/paper/2507.11847/) (2025)
- [Kullback-Leibler Maillard Sampling for Multi-armed Bandits with Bounded Rewards](https://mlsanity.com/paper/2304.14989/) (2023)
- [Logistic Bandits with tildeO(√dT) Regret without Context Diversity Assumptions](https://mlsanity.com/paper/2604.22161/) (2026)
- [Minimax Optimal Regret for Causal Logistic Bandits with Counterfactual Fairness](https://mlsanity.com/paper/2610.01377/) (2026)

## Abstract (arXiv)

In this work we consider the problem of regret minimization for logistic bandits. The main challenge of logistic bandits is reducing the dependence on a potentially large problem dependent constant kappa that can at worst scale exponentially with the norm of the unknown parameter θast. Abeille et al. (2021) have applied self-concordance of the logistic function to remove this worst-case dependence providing regret guarantees like O(dlog2(kappa)√dotμ Tlog(|X|)) where d is the dimensionality, T is the time horizon, and dotμ is the variance of the best-arm. This work improves upon this bound in the fixed arm setting by employing an experimental design procedure that achieves a minimax regret of O(√d dotμ Tlog(|X|)). Our regret bound in fact takes a tighter instance (i.e., gap) dependent regret bound for the first time in logistic bandits. We also propose a new warmup sampling algorithm that can dramatically reduce the lower order term in the regret in general and prove that it can replace the lower order term dependency on kappa to log2(kappa) for some instances. Finally, we discuss the impact of the bias of the MLE on the logistic bandit problem, providing an example where d2 lower order regret (cf., it is d for linear bandits) may not be improved as long as the MLE is used and how bias-corrected estimators may be used to make it closer to d.