Online Bayesian Persuasion Without a Clue

TL;DR

This paper introduces an online Bayesian persuasion algorithm that learns optimal signaling schemes without prior knowledge, achieving sublinear regret and establishing tight bounds in a setting where the sender is initially uninformed.

Contribution

It presents the first algorithm for online Bayesian persuasion that operates without prior knowledge, using a novel signaling scheme representation to learn receiver responses.

Findings

Achieves sublinear regret compared to optimal schemes.

Provides tight lower bounds on learning guarantees.

Establishes bounds on sample complexity for related PAC-learning problems.

Abstract

We study online Bayesian persuasion problems in which an informed sender repeatedly faces a receiver with the goal of influencing their behavior through the provision of payoff-relevant information. Previous works assume that the sender has knowledge about either the prior distribution over states of nature or receiver's utilities, or both. We relax such unrealistic assumptions by considering settings in which the sender does not know anything about the prior and the receiver. We design an algorithm that achieves sublinear regret with respect to an optimal signaling scheme, and we also provide a collection of lower bounds showing that the guarantees of such an algorithm are tight. Our algorithm works by searching a suitable space of signaling schemes in order to learn receiver's best responses. To do this, we leverage a non-standard representation of signaling schemes that allows to cleverly overcome the challenge of not knowing anything about the prior over states of nature and receiver's utilities. Finally, our results also allow to derive lower/upper bounds on the sample complexity of learning signaling schemes in a related Bayesian persuasion PAC-learning problem.