# Self-Concordant Analysis of Generalized Linear Bandits with Forgetting

arXiv: https://arxiv.org/abs/2011.00819 · HTML: https://mlsanity.com/paper/2011.00819/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Nov 2020.

## Built on by (most cited first, 29 of 29)

- [On the Theory of Reinforcement Learning with Once-per-Episode Feedback](https://mlsanity.com/paper/2105.14363/) (2021)
- [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: Almost Optimal Regret with One-Pass Update](https://mlsanity.com/paper/2507.11847/) (2025)
- [Double Doubly Robust Thompson Sampling for Generalized Linear Contextual Bandits](https://mlsanity.com/paper/2209.06983/) (2022)
- [Regret Bounds for Generalized Linear Bandits under Parameter Drift](https://mlsanity.com/paper/2103.05750/) (2021)
- [Exploration via linearly perturbed loss minimisation](https://mlsanity.com/paper/2311.07565/) (2023)
- [Almost Free: Self-concordance in Natural Exponential Families and an Application to Bandits](https://mlsanity.com/paper/2410.01112/) (2024)
- [Coverage Improvement and Fast Convergence of On-policy Preference Learning](https://mlsanity.com/paper/2601.08421/) (2026)
- [Revisiting Weighted Strategy for Non-stationary Parametric Bandits and MDPs](https://mlsanity.com/paper/2601.01069/) (2026)
- [Provably Efficient Regularized Online RLHF with Generalized Bilinear Preferences](https://mlsanity.com/paper/2602.23116/) (2026)
- [Reinforcement Learning with Segment Feedback](https://mlsanity.com/paper/2502.01876/) (2025)
- [Generalized Kernelized Bandits: A Novel Self-Normalized Bernstein-Like Dimension-Free Inequality and Regret Bounds](https://mlsanity.com/paper/2508.01681/) (2025)
- [Variance-Dependent Regret Bounds for Non-stationary Linear Bandits](https://mlsanity.com/paper/2403.10732/) (2024)
- [Near Optimal Pure Exploration in Logistic Bandits](https://mlsanity.com/paper/2410.20640/) (2024)
- [A Jointly Efficient and Optimal Algorithm for Heteroskedastic Generalized Linear Bandits with Adversarial Corruptions](https://mlsanity.com/paper/2602.10971/) (2026)
- [Best Arm Identification in Generalized Linear Bandits via Hybrid Feedback](https://mlsanity.com/paper/2605.05745/) (2026)
- [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)
- [Preference-Guided Reinforcement Learning for Efficient Exploration](https://mlsanity.com/paper/2407.06503/) (2024)
- [DAL: A Practical Prior-Free Black-Box Framework for Piecewise Stationary Bandits](https://mlsanity.com/paper/2501.19401/) (2025)
- [Reinforcement Learning from Multi-level and Episodic Human Feedback](https://mlsanity.com/paper/2504.14732/) (2025)
- [Fooling Algorithms in Non-Stationary Bandits using Belief Inertia](https://mlsanity.com/paper/2511.05620/) (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)
- [Variance-sensitive Thompson sampling for generalised linear bandits, revisited](https://mlsanity.com/paper/2606.00431/) (2026)
- [Time-Uniform Self-Normalized Concentration for Discounted Least Squares: Limits and Corrections](https://mlsanity.com/paper/2608.19643/) (2026)
- [Toward Optimal Switching Regret for Multi-Armed Bandits with Oblivious Adversary](https://mlsanity.com/paper/2609.13547/) (2026)
- [Elicitation and Decision Geometry in Single-Index Bandits](https://mlsanity.com/paper/2609.35622/) (2026)

## Abstract (arXiv)

Contextual sequential decision problems with categorical or numerical observations are ubiquitous and Generalized Linear Bandits (GLB) offer a solid theoretical framework to address them. In contrast to the case of linear bandits, existing algorithms for GLB have two drawbacks undermining their applicability. First, they rely on excessively pessimistic concentration bounds due to the non-linear nature of the model. Second, they require either non-convex projection steps or burn-in phases to enforce boundedness of the estimators. Both of these issues are worsened when considering non-stationary models, in which the GLB parameter may vary with time. In this work, we focus on self-concordant GLB (which include logistic and Poisson regression) with forgetting achieved either by the use of a sliding window or exponential weights. We propose a novel confidence-based algorithm for the maximum-likehood estimator with forgetting and analyze its perfomance in abruptly changing environments. These results as well as the accompanying numerical simulations highlight the potential of the proposed approach to address non-stationarity in GLB.