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arXiv · 2501.10722

A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits

Jiannan Li·Yiyang Yang·Yao Wang·Shaojie Tang
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Abstract

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.

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BibTeXRIS

Jiannan Li, Yiyang Yang, Yao Wang, Shaojie Tang. 2025-01-18. A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits. https://arxiv.org/abs/2501.10722

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