# Regret Bounds for Generalized Linear Bandits under Parameter Drift

arXiv: https://arxiv.org/abs/2103.05750 · HTML: https://mlsanity.com/paper/2103.05750/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- Builds on 13 of its 24 references that are in the map.
- First posted on arXiv 9 Mar 2021.

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

- [Learning to Optimize Via Posterior Sampling](https://mlsanity.com/paper/1301.2609/) (2013)
- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Weighted Linear Bandits for Non-Stationary Environments](https://mlsanity.com/paper/1909.09146/) (2019)
- [Learning to Optimize under Non-Stationarity](https://mlsanity.com/paper/1810.03024/) (2018)
- [Scalable Generalized Linear Bandits: Online Computation and Hashing](https://mlsanity.com/paper/1706.00136/) (2017)
- [Instance-Wise Minimax-Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2010.12642/) (2020)
- [Hedging the Drift: Learning to Optimize under Non-Stationarity](https://mlsanity.com/paper/1903.01461/) (2019)
- [Provably Optimal Algorithms for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/1703.00048/) (2017)
- [An Information-Theoretic Analysis for Thompson Sampling with Many Actions](https://mlsanity.com/paper/1805.11845/) (2018)
- [Self-Concordant Analysis of Generalized Linear Bandits with Forgetting](https://mlsanity.com/paper/2011.00819/) (2020)
- [Efficient Learning in Non-Stationary Linear Markov Decision Processes](https://mlsanity.com/paper/2010.12870/) (2020)
- [Algorithms for Non-Stationary Generalized Linear Bandits](https://mlsanity.com/paper/2003.10113/) (2020)
- [PG-TS: Improved Thompson Sampling for Logistic Contextual Bandits](https://mlsanity.com/paper/1805.07458/) (2018)

## Built on by (most cited first, 13 of 13)

- [Non-stationary Bandits with Knapsacks](https://mlsanity.com/paper/2205.12427/) (2022)
- [Right Now, Wrong Then: Non-Stationary Direct Preference Optimization under Preference Drift](https://mlsanity.com/paper/2407.18676/) (2024)
- [Near-Optimal Goal-Oriented Reinforcement Learning in Non-Stationary Environments](https://mlsanity.com/paper/2205.13044/) (2022)
- [Revisiting Weighted Strategy for Non-stationary Parametric Bandits and MDPs](https://mlsanity.com/paper/2601.01069/) (2026)
- [Non-Stationary Lipschitz Bandits](https://mlsanity.com/paper/2505.18871/) (2025)
- [Variance-Dependent Regret Bounds for Non-stationary Linear Bandits](https://mlsanity.com/paper/2403.10732/) (2024)
- [Revisiting Weighted Strategy for Non-stationary Parametric Bandits](https://mlsanity.com/paper/2303.02691/) (2023)
- [Weighted Sequential Bayesian Inference for Non-Stationary Linear Contextual Bandits](https://mlsanity.com/paper/2307.03587/) (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)
- [Bandits for Efficient Experimentation: Adapting to Control Group, Preferences, and Context Drifts](https://mlsanity.com/paper/2606.09802/) (2026)
- [Time-Uniform Self-Normalized Concentration for Discounted Least Squares: Limits and Corrections](https://mlsanity.com/paper/2608.19643/) (2026)

## Abstract (arXiv)

Generalized Linear Bandits (GLBs) are powerful extensions to the Linear Bandit (LB) setting, broadening the benefits of reward parametrization beyond linearity. In this paper we study GLBs in non-stationary environments, characterized by a general metric of non-stationarity known as the variation-budget or parameter-drift, denoted BT. While previous attempts have been made to extend LB algorithms to this setting, they overlook a salient feature of GLBs which flaws their results. In this work, we introduce a new algorithm that addresses this difficulty. We prove that under a geometric assumption on the action set, our approach enjoys a tildeO(BT1/3T2/3) regret bound. In the general case, we show that it suffers at most a tildeO(BT1/5T4/5) regret. At the core of our contribution is a generalization of the projection step introduced in Filippi et al. (2010), adapted to the non-stationary nature of the problem. Our analysis sheds light on central mechanisms inherited from the setting by explicitly splitting the treatment of the learning and tracking aspects of the problem.