Multi-thresholding Good Arm Identification with Bandit Feedback

• URL: http://arxiv.org/abs/2503.10386v3
• Date: Thu, 26 Jun 2025 21:38:37 GMT
• Title: Multi-thresholding Good Arm Identification with Bandit Feedback
• Authors: Xuanke Jiang, Sherief Hashima, Kohei Hatano, Eiji Takimoto,
• Abstract summary: We consider a good arm identification problem in a bandit setting with multi-objectives.<n>We propose the Multi-Thresholding UCB(MultiTUCB) algorithm with a sample complexity bound.
• Score: 1.079960007119637
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a good arm identification problem in a stochastic bandit setting with multi-objectives, where each arm $i \in [K]$ is associated with a distribution $D_i$ defined over $R^M$. For each round $t$, the player pulls an arm $i_t$ and receives an $M$-dimensional reward vector sampled according to $D_{i_t}$. The goal is to find, with high probability, an $\epsilon$-good arm whose expected reward vector is larger than $\bm{\xi} - \epsilon \mathbf{1}$, where $\bm{\xi}$ is a predefined threshold vector, and the vector comparison is component-wise. We propose the Multi-Thresholding UCB~(MultiTUCB) algorithm with a sample complexity bound. Our bound matches the existing one in the special case where $M=1$ and $\epsilon=0$. The proposed algorithm demonstrates superior performance compared to baseline approaches across synthetic and real datasets.

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