让发送方在不知接收方私有信息源的情况下，学会有效说服对方。
Learning to Persuade Privately Informed Receivers
- 通过在线学习优化信号披露策略，适应接收方的私有信息处理方式。
- 实现近似最优的后悔率 $\widetilde{O}(T^{3/4})$，依赖于状态与信号空间大小的多项式因子。
- 将复杂信念空间分割问题转化为一维变点检测，突破计算瓶颈。
贝叶斯劝说研究知情发送方如何通过策略性信息披露影响接收方行为。标准模型假设发送方是接收方唯一信息来源，但在许多实际场景中，接收方还会参考外部信息源，而发送方无法观测或控制这些源。本文研究一种在线贝叶斯劝说问题：接收方为二元动作选择者，其采用一个对发送方未知的固定信号机制。在 $T$ 轮中，发送方承诺一个信号方案并发送信号；接收方将该信号与其私有信号结合后行动，发送方仅能观察到最终行动。我们设计了一种学习算法，相对于已知接收方私有信号机制的最优发送方，实现 $ ilde{O}(T^{3/4})$ 的后悔率，且对状态空间和接收方信号字母表大小呈多项式依赖。关键洞察在于将由私有机制诱导的指数级信念空间划分问题，简化为一维变点检测问题。
原文摘要 · Abstract (English)
Bayesian persuasion studies how an informed sender can influence the behavior of a receiver through strategic information disclosure. Standard models assume the sender is the receiver's only source of information, yet in many applications receivers also consult external sources the sender can neither observe nor control. We study an online Bayesian persuasion problem in which a binary-action receiver has access to a fixed signaling scheme that is unknown to the sender. Over $T$ rounds, the sender commits to a signaling scheme and sends a signal; the receiver combines it with its private signal and acts, while the sender observes only the action. We design a learning algorithm that achieves regret $\widetilde{O}(T^{3/4})$ relative to the optimal scheme of a sender who knows the private signaling scheme of the receiver, with polynomial dependence on the sizes of the state space and the receiver's signal alphabet. Our key insight is reducing the problem of learning the exponentially large belief-space partitioning induced by the private scheme to a one-dimensional change-point detection problem.
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