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.

翻译：本文旨在构建一种新型赌博机算法，能够充分利用多维数据的潜力以及奖励函数的内在非线性特性，提供高可用且可解释的决策服务。为此，我们提出一种广义低秩张量上下文赌博机模型，其中动作由三个特征向量构成，因此可用张量表示。在该模型中，奖励通过将广义线性函数应用于动作特征张量与一个固定但未知的低管子秩参数张量的内积来确定。为有效实现探索与利用的权衡，我们提出一种名为“广义低秩张量探索子空间再精细”（G-LowTESTR）的新算法。该算法首先收集原始数据以探索决策场景中嵌入的内在低秩张量子空间信息，然后将原始问题转化为近似低维的广义线性上下文赌博机问题。严格的理论分析表明，G-LowTESTR的遗憾界优于向量化和矩阵化情形。我们通过一系列模拟实验和真实数据实验进一步验证了G-LowTESTR的有效性，凸显其利用低秩张量结构增强学习能力。