Stochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Making
This work addresses decision-making challenges in applications like digital marketing by leveraging low-rank tensor structures, offering incremental improvements over existing bandit methods.
The paper tackles the problem of multi-dimensional online decision making, such as in online recommendation and advertising, by introducing stochastic low-rank tensor bandits and proposing algorithms like tensor elimination and tensor epoch-greedy, achieving improved regret bounds and outperforming state-of-the-art methods in simulations and real data analysis.
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.