# Stochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Making

arXiv: https://arxiv.org/abs/2007.15788 · HTML: https://mlsanity.com/paper/2007.15788/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Jul 2020.

## Built on by (most cited first, 10 of 10)

- [Online Low Rank Matrix Completion](https://mlsanity.com/paper/2209.03997/) (2022)
- [Improved Regret of Linear Ensemble Sampling](https://mlsanity.com/paper/2411.03932/) (2024)
- [On High-dimensional and Low-rank Tensor Bandits](https://mlsanity.com/paper/2305.03884/) (2023)
- [Online Policy Learning and Inference by Matrix Completion](https://mlsanity.com/paper/2404.17398/) (2024)
- [Low-Rank Online Dynamic Assortment with Dual Contextual Information](https://mlsanity.com/paper/2404.17592/) (2024)
- [Efficient Generalized Low-Rank Tensor Contextual Bandits](https://mlsanity.com/paper/2311.01771/) (2023)
- [A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits](https://mlsanity.com/paper/2501.10722/) (2025)
- [Sharp analysis of linear ensemble sampling](https://mlsanity.com/paper/2602.08026/) (2026)
- [Linear Ensemble Sampling with Smaller Ensembles](https://mlsanity.com/paper/2609.13954/) (2026)
- [Low-Rank Single-Index Bandits with Unknown Links: From Matrices to Tensors](https://mlsanity.com/paper/2609.33025/) (2026)

## Abstract (arXiv)

Multi-dimensional online decision making plays a crucial role in many real applications such as online recommendation and digital marketing. In these problems, a decision at each time is a combination of choices from different types of entities. To solve it, we introduce stochastic low-rank tensor bandits, a class of bandits whose mean rewards can be represented as a low-rank tensor. We consider two settings, tensor bandits without context and tensor bandits with context. In the first setting, the platform aims to find the optimal decision with the highest expected reward, a.k.a, the largest entry of true reward tensor. In the second setting, some modes of the tensor are contexts and the rest modes are decisions, and the goal is to find the optimal decision given the contextual information. We propose two learning algorithms tensor elimination and tensor epoch-greedy for tensor bandits without context, and derive finite-time regret bounds for them. Comparing with existing competitive methods, tensor elimination has the best overall regret bound and tensor epoch-greedy has a sharper dependency on dimensions of the reward tensor. Furthermore, we develop a practically effective Bayesian algorithm called tensor ensemble sampling for tensor bandits with context. Extensive simulations and real analysis in online advertising data back up our theoretical findings and show that our algorithms outperform various state-of-the-art approaches that ignore the tensor low-rank structure.