设计激励机制让智能体主动探索未知选项，同时控制成本与误差。
Incentivized Lipschitz Bandits
- 将无限臂问题离散化，用统一网格覆盖连续空间
- 理论证明累计损失和补偿均低于线性增长，随时间呈次线性
- 适用于有上下文的复杂场景，适合研究激励机制的设计者
我们研究在连续度量空间中具有无穷多臂的多臂老虎机问题中的激励探索。不同于经典模型，决策者（委托方）通过补偿激励短视代理超越其贪婪选择进行探索，但面临奖励漂移——由激励引起的偏差反馈。我们提出新颖的激励探索算法，对无限臂空间进行均匀离散化，并证明这些算法能同时实现次线性累计后悔和次线性总补偿。具体地，我们推导出后悔和补偿的上界为 $\Tilde{O}(T^{d+1/d+2})$，其中 $d$ 表示度量空间的覆盖维数。此外，我们将结果推广至上下文老虎机，获得类似的性能保证。数值模拟验证了理论发现。
原文摘要 · Abstract (English)
We study incentivized exploration in multi-armed bandit (MAB) settings with infinitely many arms modeled as elements in continuous metric spaces. Unlike classical bandit models, we consider scenarios where the decision-maker (principal) incentivizes myopic agents to explore beyond their greedy choices through compensation, but with the complication of reward drift--biased feedback arising due to the incentives. We propose novel incentivized exploration algorithms that discretize the infinite arm space uniformly and demonstrate that these algorithms simultaneously achieve sublinear cumulative regret and sublinear total compensation. Specifically, we derive regret and compensation bounds of $\Tilde{O}(T^{d+1/d+2})$, with $d$ representing the covering dimension of the metric space. Furthermore, we generalize our results to contextual bandits, achieving comparable performance guarantees. We validate our theoretical findings through numerical simulations.
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