Variance-Dependent Regret Bounds for Non-stationary Linear Bandits

• URL: http://arxiv.org/abs/2403.10732v1
• Date: Fri, 15 Mar 2024 23:36:55 GMT
• Title: Variance-Dependent Regret Bounds for Non-stationary Linear Bandits
• Authors: Zhiyong Wang, Jize Xie, Yi Chen, John C. S. Lui, Dongruo Zhou,
• Abstract summary: 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. We introduce two novel algorithms: Restarted Weighted$textOFUL+$ and Restarted $textSAVE+$. Notably, when the total variance $V_K$ is much smaller than $K$, our algorithms outperform previous state-of-the-art results on non-stationary linear bandits under different settings.
• Score: 52.872628573907434
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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