# A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits

arXiv: https://arxiv.org/abs/2501.10722 · HTML: https://mlsanity.com/paper/2501.10722/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 38 references that are in the map.
- First posted on arXiv 18 Jan 2025.

## Builds on (most cited first, 18 of 18)

- [High-Dimensional Sparse Linear Bandits](https://mlsanity.com/paper/2011.04020/) (2020)
- [Bilinear Bandits with Low-rank Structure](https://mlsanity.com/paper/1901.02470/) (2019)
- [Doubly-Robust Lasso Bandit](https://mlsanity.com/paper/1907.11362/) (2019)
- [Low-Rank Generalized Linear Bandit Problems](https://mlsanity.com/paper/2006.02948/) (2020)
- [Sparsity-Agnostic Lasso Bandit](https://mlsanity.com/paper/2007.08477/) (2020)
- [Dynamic Batch Learning in High-Dimensional Sparse Linear Contextual Bandits](https://mlsanity.com/paper/2008.11918/) (2020)
- [Distribution-free Contextual Dynamic Pricing](https://mlsanity.com/paper/2109.07340/) (2021)
- [A Simple Unified Framework for High Dimensional Bandit Problems](https://mlsanity.com/paper/2102.09626/) (2021)
- [Efficient Frameworks for Generalized Low-Rank Matrix Bandit Problems](https://mlsanity.com/paper/2401.07298/) (2024)
- [PopArt: Efficient Sparse Regression and Experimental Design for Optimal Sparse Linear Bandits](https://mlsanity.com/paper/2210.15345/) (2022)
- [A Tractable Online Learning Algorithm for the Multinomial Logit Contextual Bandit](https://mlsanity.com/paper/2011.14033/) (2020)
- [Stochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Making](https://mlsanity.com/paper/2007.15788/) (2020)
- [Spoiled for Choice? Personalized Recommendation for Healthcare Decisions: A Multi-Armed Bandit Approach](https://mlsanity.com/paper/2009.06108/) (2020)
- [Efficient Low-Rank Matrix Estimation, Experimental Design, and Arm-Set-Dependent Low-Rank Bandits](https://mlsanity.com/paper/2402.11156/) (2024)
- [Doubly High-Dimensional Contextual Bandits: An Interpretable Model for Joint Assortment-Pricing](https://mlsanity.com/paper/2309.08634/) (2023)
- [On High-dimensional and Low-rank Tensor Bandits](https://mlsanity.com/paper/2305.03884/) (2023)
- [Filtered Poisson Process Bandit on a Continuum](https://mlsanity.com/paper/2007.09966/) (2020)
- [Stochastic Contextual Bandits with Long Horizon Rewards](https://mlsanity.com/paper/2302.00814/) (2023)

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

- [Low-Rank Single-Index Bandits with Unknown Links: From Matrices to Tensors](https://mlsanity.com/paper/2609.33025/) (2026)

## Abstract (arXiv)

Modern decision-making scenarios often involve data that is both high-dimensional and rich in higher-order contextual information, where existing bandits algorithms fail to generate effective policies. In response, we propose in this paper a generalized linear tensor bandits algorithm designed to tackle these challenges by incorporating low-dimensional tensor structures, and further derive a unified analytical framework of the proposed algorithm. Specifically, our framework introduces a convex optimization approach with the weakly decomposable regularizers, enabling it to not only achieve better results based on the tensor low-rankness structure assumption but also extend to cases involving other low-dimensional structures such as slice sparsity and low-rankness. The theoretical analysis shows that, compared to existing low-rankness tensor result, our framework not only provides better bounds but also has a broader applicability. Notably, in the special case of degenerating to low-rank matrices, our bounds still offer advantages in certain scenarios.