Minimax最优的信任感知多臂老虎机
Minimax-optimal trust-aware multi-armed bandits
AI总结：
针对现有多臂老虎机算法忽略人类信任因素导致性能下降的问题，本文提出两阶段信任感知流程，确立信任问题下的minimax遗憾值，证明其接近最优的统计保证，并通过仿真验证其优势。
摘要：
多臂老虎机（MAB）算法在序贯决策应用中取得了显著成功，其前提是人类能够完美执行推荐的策略。然而，现有方法往往忽略了人类对学习算法的信任这一关键因素。当信任不足时，人类可能会偏离推荐策略，导致学习性能不佳。受这一研究空白的驱动，我们通过将动态信任模型整合到标准MAB框架中，研究信任感知MAB问题。具体而言，该模型假设推荐策略与实际执行的策略会因人类信任程度而存在差异，而信任程度又会随推荐策略的质量演变。我们确立了存在信任问题时的minimax遗憾值，并证明了如置信上界（UCB）算法这类普通MAB算法的次优性。为克服这一局限，我们提出了一种新颖的两阶段信任感知流程，该流程可证明能获得接近最优的统计保证。我们开展了仿真研究，以说明所提算法在处理信任问题时的优势。
英文摘要：
Multi-armed bandit (MAB) algorithms have achieved significant success in sequential decision-making applications, under the premise that humans perfectly implement the recommended policy. However, existing methods often overlook the crucial factor of human trust in learning algorithms. When trust is lacking, humans may deviate from the recommended policy, leading to undesired learning performance. Motivated by this gap, we study the trust-aware MAB problem by integrating a dynamic trust model into the standard MAB framework. Specifically, it assumes that the recommended and actually implemented policy differs depending on human trust, which in turn evolves with the quality of the recommended policy. We establish the minimax regret in the presence of the trust issue and demonstrate the suboptimality of vanilla MAB algorithms such as the upper confidence bound (UCB) algorithm. To overcome this limitation, we introduce a novel two-stage trust-aware procedure that provably attains near-optimal statistical guarantees. A simulation study is conducted to illustrate the benefits of our proposed algorithm when dealing with the trust issue.
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