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- W4287702970 abstract "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. Numerical experiments back up our theoretical findings and show that our algorithms outperform various state-of-the-art approaches that ignore the tensor low-rank structure. In an online advertising application with contextual information, our tensor ensemble sampling reduces the cumulative regret by 75% compared to the benchmark method." @default.
- W4287702970 created "2022-07-26" @default.
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- W4287702970 date "2020-07-30" @default.
- W4287702970 modified "2023-09-26" @default.
- W4287702970 title "Stochastic Low-rank Tensor Bandits for Multi-dimensional Online Decision Making" @default.
- W4287702970 doi "https://doi.org/10.48550/arxiv.2007.15788" @default.
- W4287702970 hasPublicationYear "2020" @default.
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