# Algorithms for Non-Stationary Generalized Linear Bandits

arXiv: https://arxiv.org/abs/2003.10113 · HTML: https://mlsanity.com/paper/2003.10113/

## Key facts

- Cited by 24 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Mar 2020.

## Built on by (most cited first, 24 of 24)

- [Non-stationary Reinforcement Learning without Prior Knowledge: An Optimal Black-box Approach](https://mlsanity.com/paper/2102.05406/) (2021)
- [Weighted Gaussian Process Bandits for Non-stationary Environments](https://mlsanity.com/paper/2107.02371/) (2021)
- [Generalized Linear Bandits with Limited Adaptivity](https://mlsanity.com/paper/2404.06831/) (2024)
- [Non-Stationary Bandit Learning via Predictive Sampling](https://mlsanity.com/paper/2205.01970/) (2022)
- [Regret Bounds for Generalized Linear Bandits under Parameter Drift](https://mlsanity.com/paper/2103.05750/) (2021)
- [Model-Based Reinforcement Learning with Multinomial Logistic Function Approximation](https://mlsanity.com/paper/2212.13540/) (2022)
- [ANACONDA: An Improved Dynamic Regret Algorithm for Adaptive Non-Stationary Dueling Bandits](https://mlsanity.com/paper/2210.14322/) (2022)
- [Near-Optimal Goal-Oriented Reinforcement Learning in Non-Stationary Environments](https://mlsanity.com/paper/2205.13044/) (2022)
- [Linear Bandits with Memory: from Rotting to Rising](https://mlsanity.com/paper/2302.08345/) (2023)
- [Revisiting Weighted Strategy for Non-stationary Parametric Bandits and MDPs](https://mlsanity.com/paper/2601.01069/) (2026)
- [Variance-Dependent Regret Bounds for Non-stationary Linear Bandits](https://mlsanity.com/paper/2403.10732/) (2024)
- [Infinite-Horizon Reinforcement Learning with Multinomial Logistic Function Approximation](https://mlsanity.com/paper/2406.13633/) (2024)
- [MNL-Bandit in non-stationary environments](https://mlsanity.com/paper/2303.02504/) (2023)
- [Non-Stationary Contextual Bandit Learning via Neural Predictive Ensemble Sampling](https://mlsanity.com/paper/2310.07786/) (2023)
- [Tracking Most Significant Shifts in Infinite-Armed Bandits](https://mlsanity.com/paper/2502.00108/) (2025)
- [High-dimensional Nonparametric Contextual Bandit Problem](https://mlsanity.com/paper/2505.14102/) (2025)
- [Generalized Linear Bandits with Memory](https://mlsanity.com/paper/2608.15848/) (2026)
- [Bounded (O(1)) Regret Recommendation Learning via Synthetic Controls Oracle](https://mlsanity.com/paper/2301.12571/) (2023)
- [Revisiting Weighted Strategy for Non-stationary Parametric Bandits](https://mlsanity.com/paper/2303.02691/) (2023)
- [DAL: A Practical Prior-Free Black-Box Framework for Piecewise Stationary Bandits](https://mlsanity.com/paper/2501.19401/) (2025)
- [DARLING: Detection Augmented Reinforcement Learning with Non-Stationary Guarantees](https://mlsanity.com/paper/2604.16684/) (2026)
- [Nonstationary Generalized Linear Bandits with Discounted Online Mirror Descent](https://mlsanity.com/paper/2605.25590/) (2026)
- [Time-Uniform Self-Normalized Concentration for Discounted Least Squares: Limits and Corrections](https://mlsanity.com/paper/2608.19643/) (2026)
- [Bellman-Centric Learning: Near-Optimal Regret for Linear Bandits with Memory](https://mlsanity.com/paper/2610.05659/) (2026)

## Abstract (arXiv)

The statistical framework of Generalized Linear Models (GLM) can be applied to sequential problems involving categorical or ordinal rewards associated, for instance, with clicks, likes or ratings. In the example of binary rewards, logistic regression is well-known to be preferable to the use of standard linear modeling. Previous works have shown how to deal with GLMs in contextual online learning with bandit feedback when the environment is assumed to be stationary. In this paper, we relax this latter assumption and propose two upper confidence bound based algorithms that make use of either a sliding window or a discounted maximum-likelihood estimator. We provide theoretical guarantees on the behavior of these algorithms for general context sequences and in the presence of abrupt changes. These results take the form of high probability upper bounds for the dynamic regret that are of order d^2/3 G^1/3 T^2/3 , where d, T and G are respectively the dimension of the unknown parameter, the number of rounds and the number of breakpoints up to time T. The empirical performance of the algorithms is illustrated in simulated environments.