# Variance-Aware Sparse Linear Bandits

@article{Dai2022VarianceAwareSL, title={Variance-Aware Sparse Linear Bandits}, author={Yan Dai and Ruosong Wang and Simon Shaolei Du}, journal={ArXiv}, year={2022}, volume={abs/2205.13450} }

It is well-known that the worst-case minimax regret for sparse linear bandits is e Θ (cid:16) √ dT (cid:17) where d is the ambient dimension and T is the number of time steps (ignoring the dependency on sparsity). On the other hand, in the benign setting where there is no noise and the action set is the unit sphere, one can use divide-and-conquer to achieve an e O (1) regret, which is (nearly) independent of d and T . In this paper, we present the ﬁrst variance-aware regret guarantee for sparse…

## One Citation

### Contexts can be Cheap: Solving Stochastic Contextual Bandits with Linear Bandit Algorithms

- Computer ScienceArXiv
- 2022

Surprisingly, in this paper, it is shown that the stochastic contextual problem can be solved as if it is a linear bandit problem, and a novel reduction framework is established that converts every stoChastic contextuallinear bandit instance to a linearBandit instance, when the context distribution is known.

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