Persuasive Recommendations Under Unknown Prior Distribution

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."

Key Insights Distilled From

Learning to Persuade on the Fly: Robustness Against Ignorance

by You Zu,Krish... at arxiv.org 05-06-2024

https://arxiv.org/pdf/2102.10156.pdf

Deeper Inquiries

How can the proposed algorithm be extended to settings with heterogeneous receiver types or adversarial state distributions

The proposed algorithm can be extended to settings with heterogeneous receiver types by incorporating receiver-specific information into the algorithm. This can be achieved by considering different sets of actions or preferences for each receiver type, and adapting the signaling mechanism to account for these variations. By incorporating receiver-specific information, the algorithm can tailor its recommendations to each receiver type, increasing the likelihood of persuasion and improving overall performance.
In settings with adversarial state distributions, the algorithm can be modified to handle uncertainty and variability in the state information. This can be done by incorporating robust optimization techniques that account for worst-case scenarios and adversarial behavior. By considering a range of possible state distributions and designing the algorithm to perform well under the most challenging conditions, it can effectively handle adversarial state distributions and maintain persuasive capabilities.

What are the implications of the lower bound result on the fundamental limits of robust persuasion in general

The lower bound result on the fundamental limits of robust persuasion highlights the challenges and constraints inherent in persuasive communication in dynamic settings. The result demonstrates that there are inherent limitations to how effectively a sender can persuade a receiver without complete knowledge of the prior distribution. This has implications for decision-making in scenarios where persuasion is crucial, such as online recommendation systems or marketing campaigns.
The lower bound result suggests that there is a trade-off between robustness and regret in persuasion settings. It indicates that there are fundamental limits to how well a sender can persuade a receiver without complete information, and that there will always be a certain level of regret associated with robust persuasion strategies. Understanding these limits can help inform the design of more effective persuasion algorithms and strategies in practice.

Can the techniques developed in this work be applied to other online learning problems with incentive constraints, such as dynamic pricing or online auctions

The techniques developed in this work can be applied to other online learning problems with incentive constraints, such as dynamic pricing or online auctions, by adapting the algorithm to account for the specific constraints and objectives of these settings. For dynamic pricing, the algorithm can be modified to recommend pricing strategies that maximize revenue while persuading customers to make purchases. By incorporating robustness against uncertainty in customer preferences or market conditions, the algorithm can adapt to changing dynamics and make optimal pricing decisions.
In online auctions, the algorithm can be tailored to recommend bidding strategies that maximize the seller's revenue while persuading bidders to participate and place competitive bids. By considering the incentives and motivations of different bidders, the algorithm can optimize auction outcomes and achieve desirable results for both the seller and the bidders. Overall, the techniques developed in this work can be applied to a variety of online learning problems with incentive constraints, providing a framework for designing effective and persuasive algorithms in dynamic and uncertain environments.