Multi-Receiver Online Bayesian Persuasion

by   Matteo Castiglioni, et al.

Bayesian persuasion studies how an informed sender should partially disclose information to influence the behavior of a self-interested receiver. Classical models make the stringent assumption that the sender knows the receiver's utility. This can be relaxed by considering an online learning framework in which the sender repeatedly faces a receiver of an unknown, adversarially selected type. We study, for the first time, an online Bayesian persuasion setting with multiple receivers. We focus on the case with no externalities and binary actions, as customary in offline models. Our goal is to design no-regret algorithms for the sender with polynomial per-iteration running time. First, we prove a negative result: for any 0 < α≤ 1, there is no polynomial-time no-α-regret algorithm when the sender's utility function is supermodular or anonymous. Then, we focus on the case of submodular sender's utility functions and we show that, in this case, it is possible to design a polynomial-time no-(1 - 1/e)-regret algorithm. To do so, we introduce a general online gradient descent scheme to handle online learning problems with a finite number of possible loss functions. This requires the existence of an approximate projection oracle. We show that, in our setting, there exists one such projection oracle which can be implemented in polynomial time.


page 1

page 2

page 3

page 4


Bayesian Persuasion Meets Mechanism Design: Going Beyond Intractability with Type Reporting

Bayesian persuasion studies how an informed sender should partially disc...

Optimal Rates and Efficient Algorithms for Online Bayesian Persuasion

Bayesian persuasion studies how an informed sender should influence beli...

Online-Learning for min-max discrete problems

We study various discrete nonlinear combinatorial optimization problems ...

Regret-Minimizing Bayesian Persuasion

We study a Bayesian persuasion setting with binary actions (adopt and re...

Public Bayesian Persuasion: Being Almost Optimal and Almost Persuasive

Persuasion studies how an informed principal may influence the behavior ...

Sequential Information Design: Learning to Persuade in the Dark

We study a repeated information design problem faced by an informed send...

Rationality-Robust Information Design: Bayesian Persuasion under Quantal Response

We relax the receiver's full rationality assumption in Bayesian persuasi...

Please sign up or login with your details

Forgot password? Click here to reset