Variance-Dependent Regret Bounds for Non-stationary Linear Bandits
<|reference_start|>Variance-Dependent Regret Bounds for Non-stationary Linear Bandits: We investigate the non-stationary stochastic linear bandit problem where the reward distribution evolves each round. Existing algorithms characterize the non-stationarity by the total variation budget $B_K$, which is the summation of the change of the consecutive feature vectors of the linear bandits over $K$ rounds. However, such a quantity only measures the non-stationarity with respect to the expectation of the reward distribution, which makes existing algorithms sub-optimal under the general non-stationary distribution setting. In this work, we propose algorithms that utilize the variance of the reward distribution as well as the $B_K$, and show that they can achieve tighter regret upper bounds. Specifically, we introduce two novel algorithms: Restarted Weighted$\text{OFUL}^+$ and Restarted $\text{SAVE}^+$. These algorithms address cases where the variance information of the rewards is known and unknown, respectively. Notably, when the total variance $V_K$ is much smaller than $K$, our algorithms outperform previous state-of-the-art results on non-stationary stochastic linear bandits under different settings. Experimental evaluations further validate the superior performance of our proposed algorithms over existing works.<|reference_end|>
@article{wang2024variance-dependent,
    title={Variance-Dependent Regret Bounds for Non-stationary Linear Bandits},
    author={Zhiyong Wang and Jize Xie and Yi Chen and John C.S. Lui and Dongruo
  Zhou},
    journal={arXiv preprint arXiv:2403.10732},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.10732},
    primaryClass={cs.LG cs.AI}
}