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.
Interactive driving, wherein an intelligent lead vehicle equipped with real-time traffic data coordinates route choices of connected vehicles, offers a promising approach to dynamic traffic management. To address the challenge of harmonising decisions, this paper considers the strategic information revealing framework of Bayesian persuasion. Here, the principal (lead vehicle) aims to guide the agent's (connected vehicle) partially observable sequential decision making towards its own objectives by selectively revealing information, such as real-time traffic ahead, using signals. However, the agent's farsighted response to maximize its long-term reward, renders the principal's signaling strategy design computationally challenging. We propose an online structured reinforcement learning framework to synthesize computationally efficient signaling strategy which is persuasive for a far-sighted agent. The main contributions of the paper are as follows: (i) For a monotonic agent with approximate best response, we propose MAPL, a structured policy learning algorithm for faster online learning, (ii) Identification of sufficient conditions for the supermodular structure of the Q function of the principal for a monotonic agent, (iii) Identification of sufficient conditions to ensure the persuasiveness of the principal's signaling strategy, (iv) Supermodular Q learning for Principal (SQP), which leverages the supermodular structure of principal's action value to synthesize computationally efficient signaling strategy that is persuasive for a monotonic learning agent, (v) Numerical analysis considering a real-time application of Bayesian persuasive driving for lane selection demonstrates that the proposed method is 30% cost efficient for optimising travelling rewards of both the lead and connected vehicle compared to the existing methodologies for signaling strategy design.