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This research advances the theoretical boundaries of Bayesian persuasion by addressing scenarios where receivers utilize private information sources unknown to the sender. The authors propose an online learning algorithm that achieves a specific regret bound, effectively reducing complex belief-space partitioning problems to manageable change-point detection tasks. This work is significant for understanding strategic information disclosure in environments with partial observability and external data inputs.
Learning to Persuade Privately Informed Receivers
arXiv:2607.28342v1 Announce Type: cross Abstract: 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.
Abstract: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.
Computer Science and Game Theory (cs.GT); Machine Learning (cs.LG)
arXiv:2607.28342 [cs.GT]
(or arXiv:2607.28342v1 [cs.GT] for this version)
https://doi.org/10.48550/arXiv.2607.28342 Focus to learn more arXiv-issued DOI via DataCite
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