# Generalized Linear Bandits with Memory

arXiv: https://arxiv.org/abs/2608.15848 · HTML: https://mlsanity.com/paper/2608.15848/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 32 references that are in the map.
- First posted on arXiv 16 Aug 2026.

## Builds on (most cited first, 21 of 21)

- [Improved Optimistic Algorithms for Logistic Bandits](https://mlsanity.com/paper/2002.07530/) (2020)
- [Rotting Bandits](https://mlsanity.com/paper/1702.07274/) (2017)
- [Jointly Efficient and Optimal Algorithms for Logistic Bandits](https://mlsanity.com/paper/2201.01985/) (2022)
- [Efficient Learning in Large-Scale Combinatorial Semi-Bandits](https://mlsanity.com/paper/1406.7443/) (2014)
- [A Unified Confidence Sequence for Generalized Linear Models, with Applications to Bandits](https://mlsanity.com/paper/2407.13977/) (2024)
- [Blocking Bandits](https://mlsanity.com/paper/1907.11975/) (2019)
- [Stochastic Bandits with Delay-Dependent Payoffs](https://mlsanity.com/paper/1910.02757/) (2019)
- [Algorithms for Non-Stationary Generalized Linear Bandits](https://mlsanity.com/paper/2003.10113/) (2020)
- [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)
- [Rebounding Bandits for Modeling Satiation Effects](https://mlsanity.com/paper/2011.06741/) (2020)
- [Stochastic Rising Bandits](https://mlsanity.com/paper/2212.03798/) (2022)
- [Multi-armed Bandit Problem with Known Trend](https://mlsanity.com/paper/1508.07091/) (2015)
- [Combinatorial Neural Bandits](https://mlsanity.com/paper/2306.00242/) (2023)
- [Generalized Linear Bandits: Almost Optimal Regret with One-Pass Update](https://mlsanity.com/paper/2507.11847/) (2025)
- [Improved Online Confidence Bounds for Multinomial Logistic Bandits](https://mlsanity.com/paper/2502.10020/) (2025)
- [Confidence Sequences for Generalized Linear Models via Regret Analysis](https://mlsanity.com/paper/2504.16555/) (2025)
- [Almost Free: Self-concordance in Natural Exponential Families and an Application to Bandits](https://mlsanity.com/paper/2410.01112/) (2024)
- [Upper Confidence Bounds for Combining Stochastic Bandits](https://mlsanity.com/paper/2012.13115/) (2020)
- [Revisiting Weighted Strategy for Non-stationary Parametric Bandits and MDPs](https://mlsanity.com/paper/2601.01069/) (2026)
- [Combinatorial Logistic Bandits](https://mlsanity.com/paper/2410.17075/) (2024)

## Built on by (most cited first, 1 of 1)

- [Block Optimism for Nonstationary Bandits with Latent Linear Dynamics](https://mlsanity.com/paper/2610.00911/) (2026)

## Abstract (arXiv)

We study generalized linear bandits with memory, an endogenous non-stationary setting in which rewards depend on past actions through a finite memory matrix. Building on prior work for linear models (Clerici et al., 2024), we show that the previously known tildeO(T3/4) regret bound stems from a loose analysis, and we provide a sharpened analysis that recovers a tildeO(√T) regret rate in the linear case. We then extend this improvement to generalized linear models and propose a block-wise algorithm based on shrunken confidence bounds. Our algorithm achieves a regret bound of tildeOleft(√mT + d√T + √kappa, d2 m1/4 T1/4 + kappa d2 right), where d denotes the feature dimension, m the memory length, and kappa a curvature parameter of the link function. This attains a √T-type rate despite nonlinear rewards and memory effects. To the best of our knowledge, this analysis provides a unified treatment of memory-induced non-stationarity and nonlinear link functions, while ensuring that the leading regret term is independent of the curvature of the link function. We conduct numerical experiments that are consistent with our theoretical findings.