学习如何说服一个有偏见的接收者
Learning to Persuade a Biased Receiver
AI总结：
研究重复信息设计问题，接收者系统性偏见影响信念更新，提出安全探索算法以学习偏见并维持说服价值，实现O(log log T)的最优 regret。
摘要：
我们研究了一个重复信息设计设置，在此设置中，接收者同时也是决策者，其信念更新以系统性偏见方式进行。更具体地说，模型中的扭曲后验可以表示为先验和贝叶斯后验的凸组合，由一个固定但未知的参数决定。在重复互动中，发送者选择说服信号方案，仅观察接收者的行为，并试图最小化相对于全信息 oracle 的遗憾。我们提出了一种安全探索算法，用于学习接收者的偏见同时保持高说服价值。该算法利用探测的不对称成本：保守探测仅导致局部损失，而过度激进的探测可能导致失去说服机会。对于一般的有限状态和动作空间以及任意有界的效用，我们的方法实现了O(log log T)的遗憾。一个匹配的Ω(log log T)下界表明，这一速率是最佳的。我们进一步讨论了对接收者福利的影响，以及扩展到联合未知先验和偏置，以及具有时间变化先验和效用的上下文设置。
英文摘要：
We study a repeated information design setting in which the receiver, who is also the decision-maker, updates beliefs in a systematically biased way. More specifically, a distorted posterior in our model can be written as a convex combination of the prior and the Bayesian posterior, governed by a fixed but unknown parameter. Over repeated interactions, the sender chooses persuasive signaling schemes, observes only the receiver's realized actions, and seeks to minimize regret relative to a full-information oracle that knows the receiver's biased updating rule. We propose a safe exploration algorithm for learning the receiver's bias while maintaining high persuasion value. The algorithm exploits the asymmetric cost of probing: conservative probes incur only local loss, whereas overly aggressive probes may lose the persuasive opportunity entirely. For general finite state and action spaces and arbitrary bounded utilities, our method achieves $O(\log\log T)$ regret. A matching $Ω(\log\log T)$ lower bound shows that this rate is optimal. We further discuss the influence on receiver welfare, as well as extensions to jointly unknown prior and bias, and contextual settings with time-varying priors and utilities.
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。
