A Unified Regularization Approach to High-Dimensional Generalized Tensor Bandits

TL;DR

This paper introduces a unified regularization framework for high-dimensional tensor bandits, leveraging low-dimensional tensor structures to improve decision-making policies with theoretical guarantees.

Contribution

It proposes a generalized linear tensor bandits algorithm with a convex optimization approach that unifies various low-dimensional structures, extending beyond low-rankness.

Findings

Achieves better regret bounds under tensor low-rankness.

Extends applicability to slice sparsity and other structures.

Provides improved theoretical guarantees over existing methods.

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.