A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits

Fuente: arXiv
Salvato in:
Dettagli Bibliografici
Autori principali: Li, Jiannan, Yang, Yiyang, Wang, Yao, Tang, Shaojie
Natura: Preprint
Pubblicazione: 2025
Soggetti:
Accesso online:
Tags: Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
_version_ 1866915117328760832
author Li, Jiannan
Yang, Yiyang
Wang, Yao
Tang, Shaojie
author_facet Li, Jiannan
Yang, Yiyang
Wang, Yao
Tang, Shaojie
contents 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.
format Preprint
id arxiv_https___arxiv_org_abs_2501_10722
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits
Li, Jiannan
Yang, Yiyang
Wang, Yao
Tang, Shaojie
Machine Learning
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.
title A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits
topic Machine Learning
url https://arxiv.org/abs/2501.10722