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Information Design with Unknown Prior

Ce Li, Tao Lin

TL;DR

This work tackles information design when the information designer does not know the receiver's prior over world states. It introduces learning algorithms that infer the unknown prior from receivers' actions over $T$ periods and then deploy robust signaling schemes that are near-optimal for the true prior. In the general case, the designer attains a tight regret rate of $\Theta(\log T)$, while in the practically important binary-action setting, a faster rate of $\Theta(\log \log T)$ is achievable and proven optimal. The methods combine a binary-search-based learning of the prior with robustification of signaling, yielding fast convergence and practical effectiveness for sequential persuasion under uncertainty.

Abstract

Information designers, such as online platforms, often do not know the beliefs of their receivers. We design learning algorithms so that the information designer can learn the receivers' prior belief from their actions through repeated interactions. Our learning algorithms achieve no regret relative to the optimality for the known prior at a fast speed, achieving a tight regret bound $Θ(\log T)$ in general and a tight regret bound $Θ(\log \log T)$ in the important special case of binary actions.

Information Design with Unknown Prior

TL;DR

This work tackles information design when the information designer does not know the receiver's prior over world states. It introduces learning algorithms that infer the unknown prior from receivers' actions over periods and then deploy robust signaling schemes that are near-optimal for the true prior. In the general case, the designer attains a tight regret rate of , while in the practically important binary-action setting, a faster rate of is achievable and proven optimal. The methods combine a binary-search-based learning of the prior with robustification of signaling, yielding fast convergence and practical effectiveness for sequential persuasion under uncertainty.

Abstract

Information designers, such as online platforms, often do not know the beliefs of their receivers. We design learning algorithms so that the information designer can learn the receivers' prior belief from their actions through repeated interactions. Our learning algorithms achieve no regret relative to the optimality for the known prior at a fast speed, achieving a tight regret bound in general and a tight regret bound in the important special case of binary actions.
Paper Structure (25 sections, 20 theorems, 124 equations, 5 algorithms)

This paper contains 25 sections, 20 theorems, 124 equations, 5 algorithms.

Table of Contents

  1. Introduction
  2. Related Literature
  3. Models and Preliminaries
  4. Models
  5. Robustification of Signaling Schemes
  6. Fast Learning to Persuade Receivers: General Case
  7. $O(\log T)$ Regret Upper Bound
  8. $\Omega(\log T)$ Regret Lower Bound
  9. Faster Learning to Persuade Receivers: Binary-Action Case
  10. $O(\log \log T)$ Regret Upper Bound
  11. $\Omega(\log \log T)$ Regret Lower Bound
  12. Conclusion and Discussion
  13. Useful Lemmas
  14. Robustification of Signaling Scheme: Proof of Lemma \ref{['lem:robust-pi']}
  15. Proofs in Section \ref{['sec:prior-aware']}
  16. ...and 10 more sections

Key Result

Lemma 1

Assume ass:prior-p0 and ass:D. Suppose $\|\hat{\mu} - \mu^* \|_1 \le \varepsilon \le \frac{p_0^2 D}{2}$. Any persuasive signaling scheme $\hat{\pi}$ for prior $\hat{\mu}$ can be converted into into another direct signaling scheme $\tilde{\pi}$ such that

Theorems & Definitions (47)

  • Lemma 1: Robustification
  • Lemma 2
  • proof
  • Lemma 3
  • proof
  • Claim 1
  • proof
  • Theorem 1
  • proof
  • Theorem 2
  • ...and 37 more