在多输出线性模型中，高效识别非支配臂集合。
Bandit Pareto Set Identification in a Multi-Output Linear Model
- 基于最优设计的算法，自适应采样以识别非支配臂。
- 理论证明任务难度仅由h个关键臂的次优间隙决定。
- 适用于多目标优化与自适应实验设计场景。
我们研究结构化多输出线性带子模型中的帕累托集识别（PSI）问题。在此设定中，每条臂对应一个属于ℝ^h的特征向量，其均值向量ℝ^d通过一个共同的未知矩阵Θ∈ℝ^{h×d}线性依赖于该特征向量。目标是通过自适应地从各臂收集样本，识别出非支配臂的集合。本文提出了首个基于最优设计的PSI算法，在固定预算和固定置信度两种设置下均提供了近乎最优的保证。值得注意的是，我们证明了这些任务的难度主要取决于h个臂的次优间隙。理论结果在合成数据和真实数据集上进行了广泛的基准测试验证。
原文摘要 · Abstract (English)
We study the Pareto Set Identification (PSI) problem in a structured multi-output linear bandit model. In this setting, each arm is associated a feature vector belonging to $\mathbb{R}^h$, and its mean vector in $\mathbb{R}^d$ linearly depends on this feature vector through a common unknown matrix $Θ\in \mathbb{R}^{h \times d}$. The goal is to identify the set of non-dominated arms by adaptively collecting samples from the arms. We introduce and analyze the first optimal design-based algorithms for PSI, providing nearly optimal guarantees in both the fixed-budget and the fixed-confidence settings. Notably, we show that the difficulty of these tasks mainly depends on the sub-optimality gaps of $h$ arms only. Our theoretical results are supported by an extensive benchmark on synthetic and real-world datasets.
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