# Sequential Information Design: Learning to Persuade in the Dark

arXiv: https://arxiv.org/abs/2209.03927 · HTML: https://mlsanity.com/paper/2209.03927/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 39 references that are in the map.
- First posted on arXiv 8 Sep 2022.

## Builds on (most cited first, 16 of 16)

- [Hindsight and Sequential Rationality of Correlated Play](https://mlsanity.com/paper/2012.05874/) (2020)
- [Simple Uncoupled No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium](https://mlsanity.com/paper/2104.01520/) (2021)
- [No-Regret Learning Dynamics for Extensive-Form Correlated Equilibrium](https://mlsanity.com/paper/2004.00603/) (2020)
- [Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning](https://mlsanity.com/paper/2202.10678/) (2022)
- [Bandit Linear Optimization for Sequential Decision Making and Extensive-Form Games](https://mlsanity.com/paper/2103.04546/) (2021)
- [Learning to Persuade on the Fly: Robustness Against Ignorance](https://mlsanity.com/paper/2102.10156/) (2021)
- [Bayesian Persuasion in Sequential Decision-Making](https://mlsanity.com/paper/2106.05137/) (2021)
- [Multi-Receiver Online Bayesian Persuasion](https://mlsanity.com/paper/2106.06480/) (2021)
- [Targeting and Signaling in Ad Auctions](https://mlsanity.com/paper/1708.00611/) (2017)
- [Hardness Results for Signaling in Bayesian Zero-Sum and Network Routing Games](https://mlsanity.com/paper/1512.03543/) (2015)
- [Signaling in Bayesian Network Congestion Games: the Subtle Power of Symmetry](https://mlsanity.com/paper/2002.05190/) (2020)
- [Bayesian Persuasion Meets Mechanism Design: Going Beyond Intractability with Type Reporting](https://mlsanity.com/paper/2202.00605/) (2022)
- [Persuading Voters: It's Easy to Whisper, It's Hard to Speak Loud](https://mlsanity.com/paper/1908.10620/) (2019)
- [Persuading Voters in District-based Elections](https://mlsanity.com/paper/2012.05002/) (2020)
- [Public Signaling in Bayesian Ad Auctions](https://mlsanity.com/paper/2201.09728/) (2022)
- [Signaling in Posted Price Auctions](https://mlsanity.com/paper/2201.12183/) (2022)

## Built on by (most cited first, 9 of 9)

- [Monitored Markov Decision Processes](https://mlsanity.com/paper/2402.06819/) (2024)
- [Information Design in Multi-Agent Reinforcement Learning](https://mlsanity.com/paper/2305.06807/) (2023)
- [Markov Persuasion Processes: Learning to Persuade from Scratch](https://mlsanity.com/paper/2402.03077/) (2024)
- [Algorithmic Persuasion Through Simulation](https://mlsanity.com/paper/2311.18138/) (2023)
- [Learning to Mitigate Externalities: the Coase Theorem with Hindsight Rationality](https://mlsanity.com/paper/2406.19824/) (2024)
- [Stochastic Principal-Agent Problems: Efficient Computation and Learning](https://mlsanity.com/paper/2306.03832/) (2023)
- [Provably Efficient Algorithm for Best Scoring Rule Identification in Online Principal-Agent Information Acquisition](https://mlsanity.com/paper/2505.17379/) (2025)
- [The Sample Complexity of Online Strategic Decision Making with Information Asymmetry and Knowledge Transportability](https://mlsanity.com/paper/2506.09940/) (2025)
- [Structured Reinforcement Learning for Bayesian Persuasion : Application to Intelligent Interactive Driving](https://mlsanity.com/paper/2607.13576/) (2026)

## Abstract (arXiv)

We study a repeated information design problem faced by an informed sender who tries to influence the behavior of a self-interested receiver. We consider settings where the receiver faces a sequential decision making (SDM) problem. At each round, the sender observes the realizations of random events in the SDM problem. This begets the challenge of how to incrementally disclose such information to the receiver to persuade them to follow (desirable) action recommendations. We study the case in which the sender does not know random events probabilities, and, thus, they have to gradually learn them while persuading the receiver. We start by providing a non-trivial polytopal approximation of the set of sender's persuasive information structures. This is crucial to design efficient learning algorithms. Next, we prove a negative result: no learning algorithm can be persuasive. Thus, we relax persuasiveness requirements by focusing on algorithms that guarantee that the receiver's regret in following recommendations grows sub-linearly. In the full-feedback setting -- where the sender observes all random events realizations -- , we provide an algorithm with tildeO(√T) regret for both the sender and the receiver. Instead, in the bandit-feedback setting -- where the sender only observes the realizations of random events actually occurring in the SDM problem -- , we design an algorithm that, given an α ∈ [1/2, 1] as input, ensures tildeO(Tα) and tildeO( T^max  α, 1-fracα2  ) regrets, for the sender and the receiver respectively. This result is complemented by a lower bound showing that such a regrets trade-off is essentially tight.