多目标环境下高效识别优质臂，提升决策准确率。
Multi-thresholding Good Arm Identification with Bandit Feedback
- 设计多阈值上置信界算法，动态筛选最优选项
- 理论证明样本复杂度与单目标情况一致
- 在真实和合成数据上均优于现有方法
我们研究了多目标随机老虎机中的优质臂识别问题，每个臂 $i \in [K]$ 对应一个定义在 $R^M$ 上的分布 $D_i$。每轮玩家选择一个臂 $i_t$，并获得由 $D_{i_t}$ 采样的 $M$ 维奖励向量。目标是高概率地找到一个 $ε$-优质臂，其期望奖励向量在分量上大于阈值向量 $\bmξ - ε\mathbf{1}$。我们提出了多阈值上置信界（MultiTUCB）算法，并给出了样本复杂度上界。该上界在 $M=1$ 且 $ε=0$ 的特殊情况下与已有结果一致。实验表明，该算法在合成与真实数据集上均显著优于基线方法。
原文摘要 · Abstract (English)
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 $ε$-good arm whose expected reward vector is larger than $\bmξ - ε\mathbf{1}$, where $\bmξ$ 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 $ε=0$. The proposed algorithm demonstrates superior performance compared to baseline approaches across synthetic and real datasets.
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