# Efficient Generalized Low-Rank Tensor Contextual Bandits

arXiv: https://arxiv.org/abs/2311.01771 · HTML: https://mlsanity.com/paper/2311.01771/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 17 of its 62 references that are in the map.
- First posted on arXiv 3 Nov 2023.

## Builds on (most cited first, 17 of 17)

- [Bilinear Bandits with Low-rank Structure](https://mlsanity.com/paper/1901.02470/) (2019)
- [Low-Rank Generalized Linear Bandit Problems](https://mlsanity.com/paper/2006.02948/) (2020)
- [Stochastic Low-Rank Bandits](https://mlsanity.com/paper/1712.04644/) (2017)
- [Stochastic Rank-1 Bandits](https://mlsanity.com/paper/1608.03023/) (2016)
- [Solving Bernoulli Rank-One Bandits with Unimodal Thompson Sampling](https://mlsanity.com/paper/1912.03074/) (2019)
- [A Simple Unified Framework for High Dimensional Bandit Problems](https://mlsanity.com/paper/2102.09626/) (2021)
- [Stochastic Bandits with Context Distributions](https://mlsanity.com/paper/1906.02685/) (2019)
- [A Tractable Online Learning Algorithm for the Multinomial Logit Contextual Bandit](https://mlsanity.com/paper/2011.14033/) (2020)
- [Bandit Algorithms for Precision Medicine](https://mlsanity.com/paper/2108.04782/) (2021)
- [Low-rank Bandits with Latent Mixtures](https://mlsanity.com/paper/1609.01508/) (2016)
- [Bernoulli Rank-1 Bandits for Click Feedback](https://mlsanity.com/paper/1703.06513/) (2017)
- [Stochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Making](https://mlsanity.com/paper/2007.15788/) (2020)
- [On High-dimensional and Low-rank Tensor Bandits](https://mlsanity.com/paper/2305.03884/) (2023)
- [Best Arm Identification in Graphical Bilinear Bandits](https://mlsanity.com/paper/2012.07641/) (2020)
- [Adaptive Policies for Perimeter Surveillance Problems](https://mlsanity.com/paper/1810.02176/) (2018)
- [Filtered Poisson Process Bandit on a Continuum](https://mlsanity.com/paper/2007.09966/) (2020)
- [Modeling Dynamic User Interests: A Neural Matrix Factorization Approach](https://mlsanity.com/paper/2102.06602/) (2021)

## 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)

In this paper, we aim to build a novel bandits algorithm that is capable of fully harnessing the power of multi-dimensional data and the inherent non-linearity of reward functions to provide high-usable and accountable decision-making services. To this end, we introduce a generalized low-rank tensor contextual bandits model in which an action is formed from three feature vectors, and thus can be represented by a tensor. In this formulation, the reward is determined through a generalized linear function applied to the inner product of the action's feature tensor and a fixed but unknown parameter tensor with a low tubal rank. To effectively achieve the trade-off between exploration and exploitation, we introduce a novel algorithm called "Generalized Low-Rank Tensor Exploration Subspace then Refine" (G-LowTESTR). This algorithm first collects raw data to explore the intrinsic low-rank tensor subspace information embedded in the decision-making scenario, and then converts the original problem into an almost lower-dimensional generalized linear contextual bandits problem. Rigorous theoretical analysis shows that the regret bound of G-LowTESTR is superior to those in vectorization and matricization cases. We conduct a series of simulations and real data experiments to further highlight the effectiveness of G-LowTESTR, leveraging its ability to capitalize on the low-rank tensor structure for enhanced learning.