组合老虎机的最优臂消除算法
Optimal Arm Elimination Algorithms for Combinatorial Bandits
AI总结：
针对组合老虎机中臂消除方法适配难的问题，提出将臂分为三类并结合显式探索的新型消除方案，在两种组合老虎机场景下实现近最优遗憾值，还给出匹配下界。
摘要：
组合老虎机将经典老虎机框架扩展至学习者每轮选择多个臂的场景，其应用动机来自在线推荐、商品组合优化等场景。尽管上置信界（UCB）算法的扩展在此场景下自然而然地出现，但适配臂消除方法却被证明更具挑战性。我们提出了一种新颖的消除方案，该方案将臂划分为三类（已确认臂、活跃臂、已消除臂），并引入显式探索机制来更新这些集合。我们在两种场景下验证了算法的有效性：具有通用图反馈的组合多臂老虎机，以及组合线性上下文老虎机。在这两种场景下，我们的方法都能达到接近最优的遗憾值，而基于UCB的方法因显式探索不足可被证明会失效。我们还给出了匹配的下界。
英文摘要：
Combinatorial bandits extend the classical bandit framework to settings where the learner selects multiple arms in each round, motivated by applications such as online recommendation and assortment optimization. While extensions of upper confidence bound (UCB) algorithms arise naturally in this context, adapting arm elimination methods has proved more challenging. We introduce a novel elimination scheme that partitions arms into three categories (confirmed, active, and eliminated), and incorporates explicit exploration to update these sets. We demonstrate the efficacy of our algorithm in two settings: the combinatorial multi-armed bandit with general graph feedback, and the combinatorial linear contextual bandit. In both cases, our approach achieves near-optimal regret, whereas UCB-based methods can provably fail due to insufficient explicit exploration. Matching lower bounds are also provided.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
