Core Concepts
The sender aims to make persuasive action recommendations to the receiver over time, while gradually learning the unknown prior distribution of the payoff-relevant state.
Abstract
The content describes a repeated persuasion setting between a sender and a receiver, where the sender observes a payoff-relevant state drawn from an unknown prior distribution at each time step, and shares information about the state with the receiver, who then chooses an action. The sender seeks to persuade the receiver into choosing actions that are aligned with the sender's preference by selectively sharing information about the state.
In contrast to the standard persuasion setting, the sender does not know the prior distribution and has to learn it over time. The key challenge is to design a signaling algorithm that is persuasive (i.e., the receiver finds it optimal to follow the recommendations) and simultaneously achieves low regret against the optimal persuasion mechanism with the knowledge of the prior distribution.
The paper proposes the Robustness Against Ignorance (Rai) algorithm, which maintains a set of candidate priors and chooses a persuasion scheme that is simultaneously persuasive for all of them. The authors show that Rai is efficient, persuasive with high probability, and achieves an optimal regret bound of O(√T log T), where T is the time horizon. They also prove a matching lower bound, showing that no algorithm can achieve regret better than Ω(√T), even with significantly relaxed persuasiveness requirements.
Stats
The state space Ω is a known finite set.
The action space A is a known finite set.
The sender's utility function v(ω, a) is bounded in [0, 1] for all ω ∈ Ω and a ∈ A.
The receiver's utility function u(ω, a) is known.
Quotes
"The core philosophy behind the design of our algorithm is to leverage robustness against the sender's ignorance of the prior."
"Our results contribute to the work on online learning that seeks to evaluate the value of knowing the underlying distributional parameters in settings with repeated interactions."