Efficient Algorithms for Generalized Linear Bandits with Heavy-tailed Rewards

• URL: http://arxiv.org/abs/2310.18701v1
• Date: Sat, 28 Oct 2023 13:01:10 GMT
• Title: Efficient Algorithms for Generalized Linear Bandits with Heavy-tailed Rewards
• Authors: Bo Xue, Yimu Wang, Yuanyu Wan, Jinfeng Yi, Lijun Zhang
• Abstract summary: We propose two novel algorithms based on truncation and mean of medians. Our truncation-based algorithm supports online learning, distinguishing it from existing truncation-based approaches. Our algorithms improve the regret bounds by a logarithmic factor compared to existing algorithms when $epsilon=1$.
• Score: 40.99322897009357
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: This paper investigates the problem of generalized linear bandits with heavy-tailed rewards, whose $(1+\epsilon)$-th moment is bounded for some $\epsilon\in (0,1]$. Although there exist methods for generalized linear bandits, most of them focus on bounded or sub-Gaussian rewards and are not well-suited for many real-world scenarios, such as financial markets and web-advertising. To address this issue, we propose two novel algorithms based on truncation and mean of medians. These algorithms achieve an almost optimal regret bound of $\widetilde{O}(dT^{\frac{1}{1+\epsilon}})$, where $d$ is the dimension of contextual information and $T$ is the time horizon. Our truncation-based algorithm supports online learning, distinguishing it from existing truncation-based approaches. Additionally, our mean-of-medians-based algorithm requires only $O(\log T)$ rewards and one estimator per epoch, making it more practical. Moreover, our algorithms improve the regret bounds by a logarithmic factor compared to existing algorithms when $\epsilon=1$. Numerical experimental results confirm the merits of our algorithms.

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