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Meta-Learning for Repeated Bayesian Persuasion

Ata Poyraz Turna, Asrin Efe Yorulmaz, Tamer Başar

Abstract

Classical Bayesian persuasion studies how a sender influences receivers through carefully designed signaling policies within a single strategic interaction. In many real-world environments, such interactions are repeated across multiple games, creating opportunities to exploit structural similarity across tasks. In this work, we introduce Meta-Persuasion algorithms, establishing the first line of theoretical results for both full-feedback and bandit-feedback settings in the Online Bayesian Persuasion (OBP) and Markov Persuasion Process (MPP) frameworks. We show that our proposed meta-persuasion algorithms achieve provably sharper regret rates under natural notions of task similarity, improving upon the best-known convergence rates for both OBP and MPP. At the same time, they recover the standard single-game guarantees when the sequence of games is picked arbitrarily. Finally, we complement our theoretical analysis with numerical experiments that highlight our regret improvements and the benefits of meta-learning in repeated persuasion environments.

Meta-Learning for Repeated Bayesian Persuasion

Abstract

Classical Bayesian persuasion studies how a sender influences receivers through carefully designed signaling policies within a single strategic interaction. In many real-world environments, such interactions are repeated across multiple games, creating opportunities to exploit structural similarity across tasks. In this work, we introduce Meta-Persuasion algorithms, establishing the first line of theoretical results for both full-feedback and bandit-feedback settings in the Online Bayesian Persuasion (OBP) and Markov Persuasion Process (MPP) frameworks. We show that our proposed meta-persuasion algorithms achieve provably sharper regret rates under natural notions of task similarity, improving upon the best-known convergence rates for both OBP and MPP. At the same time, they recover the standard single-game guarantees when the sequence of games is picked arbitrarily. Finally, we complement our theoretical analysis with numerical experiments that highlight our regret improvements and the benefits of meta-learning in repeated persuasion environments.
Paper Structure (26 sections, 27 theorems, 137 equations, 4 figures, 8 algorithms)

This paper contains 26 sections, 27 theorems, 137 equations, 4 figures, 8 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Preliminaries
  4. Online Bayesian Persuasion
  5. Markov Persuasion Processes
  6. Meta-Learning Across Repeated Games
  7. The Meta-Learning for Online Bayesian Persuasion
  8. Full Feedback Setting
  9. Partial Feedback Setting
  10. The Meta-Learning for Markov Persuasion Processes
  11. Estimators and Confidence Bounds for Meta-Learning in Markov Persuasion Processes
  12. Full Feedback Setting
  13. Partial Feedback Setting
  14. Numerical Results
  15. Numerical Results for Online Bayesian Persuasion
  16. ...and 11 more sections

Key Result

Theorem 3.1

For any set $\mathcal{J} \subset \mathbb{R}^{K}$ and any point $\bar{z}$ in its convex hull $\bar{\mathcal{J}}$, there exist at most $K+1$ points $z^{1},\ldots,z^{n} \in \mathcal{J}$ with $n \le K+1$ such that $z = \sum_{i=1}^{n} \lambda_{i}\, x^{i}$, where $\lambda_{i} \ge 0$ and $\sum_{i=1}^{n} \l

Figures (4)

  • Figure 1: Illustration of the Carathéodory oracle used in Algorithms \ref{['alg:omd-tuning-fb']} and \ref{['alg:omd-tuning']}.
  • Figure :
  • Figure :
  • Figure :

Theorems & Definitions (46)

  • Theorem 3.1: Carathéodory's Theorem
  • Theorem 3.2
  • Theorem 3.3
  • Corollary 3.1: Corollary 5.1 in MetaLearningBandits
  • Lemma 4.1: Lemma 1, MarkovPersuasionScratch2025
  • Theorem 4.1
  • Theorem 4.2
  • Theorem 4.3
  • Lemma A.1
  • Lemma A.2
  • ...and 36 more