Learning to Persuade a Biased Receiver

2026-05-14

AI Summary

This work addresses repeated information design where the receiver updates beliefs with an unknown but fixed systematic bias, and the sender must dynamically craft signals to achieve effective persuasion based solely on observed actions. The paper proposes a safe exploration algorithm that leverages the asymmetric cost structure between conservative and aggressive probing to simultaneously ensure high persuasive value and enable online learning of the bias. Built upon Bayesian modeling with distorted posteriors and information design theory, the method achieves an $O(\log\log T)$ regret upper bound in general finite state-action spaces under bounded utilities, and establishes a matching $\Omega(\log\log T)$ lower bound, thereby proving the optimality of this rate.

Abstract

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.

Problem

• information design
• biased belief updating
• persuasion
• regret minimization
• repeated interaction

Innovation

• information design
• biased belief updating
• safe exploration
• persuasion
• regret minimization