Linear Bandits with Limited Adaptivity and Learning Distributional Optimal Design

• URL: http://arxiv.org/abs/2007.01980v3
• Date: Fri, 23 Apr 2021 13:01:03 GMT
• Title: Linear Bandits with Limited Adaptivity and Learning Distributional Optimal Design
• Authors: Yufei Ruan, Jiaqi Yang, Yuan Zhou
• Abstract summary: We study the impact of adaptivity constraints to linear contextual bandits, a central problem in online active learning. We show that, when the context vectors are adversarially chosen in $d$-dimensional linear contextual bandits, the learner needs $O(d log d log T)$ policy switches to achieve the minimax-optimal regret.
• Score: 12.465883735626605
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Motivated by practical needs such as large-scale learning, we study the impact of adaptivity constraints to linear contextual bandits, a central problem in online active learning. We consider two popular limited adaptivity models in literature: batch learning and rare policy switches. We show that, when the context vectors are adversarially chosen in $d$-dimensional linear contextual bandits, the learner needs $O(d \log d \log T)$ policy switches to achieve the minimax-optimal regret, and this is optimal up to $\mathrm{poly}(\log d, \log \log T)$ factors; for stochastic context vectors, even in the more restricted batch learning model, only $O(\log \log T)$ batches are needed to achieve the optimal regret. Together with the known results in literature, our results present a complete picture about the adaptivity constraints in linear contextual bandits. Along the way, we propose the distributional optimal design, a natural extension of the optimal experiment design, and provide a both statistically and computationally efficient learning algorithm for the problem, which may be of independent interest.

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