# Learning to Persuade on the Fly: Robustness Against Ignorance

arXiv: https://arxiv.org/abs/2102.10156 · HTML: https://mlsanity.com/paper/2102.10156/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 20 of its 57 references that are in the map.
- First posted on arXiv 19 Feb 2021.

## Builds on (most cited first, 20 of 20)

- [Strategic Classification from Revealed Preferences](https://mlsanity.com/paper/1710.07887/) (2017)
- [Online Convex Optimization with Stochastic Constraints](https://mlsanity.com/paper/1708.03741/) (2017)
- [Linear Stochastic Bandits Under Safety Constraints](https://mlsanity.com/paper/1908.05814/) (2019)
- [Bandits with concave rewards and convex knapsacks](https://mlsanity.com/paper/1402.5758/) (2014)
- [What Doubling Tricks Can and Can't Do for Multi-Armed Bandits](https://mlsanity.com/paper/1803.06971/) (2018)
- [Stochastic Bandits with Linear Constraints](https://mlsanity.com/paper/2006.10185/) (2020)
- [Online Convex Optimization with Time-Varying Constraints](https://mlsanity.com/paper/1702.04783/) (2017)
- [Bayesian Incentive-Compatible Bandit Exploration](https://mlsanity.com/paper/1502.04147/) (2015)
- [Online convex optimization for cumulative constraints](https://mlsanity.com/paper/1802.06472/) (2018)
- [Bayesian Exploration: Incentivizing Exploration in Bayesian Games](https://mlsanity.com/paper/1602.07570/) (2016)
- [Safe Linear Thompson Sampling with Side Information](https://mlsanity.com/paper/1911.02156/) (2019)
- [Stage-wise Conservative Linear Bandits](https://mlsanity.com/paper/2010.00081/) (2020)
- [Safe Linear Stochastic Bandits](https://mlsanity.com/paper/1911.09501/) (2019)
- [Algorithmic Bayesian Persuasion](https://mlsanity.com/paper/1503.05988/) (2015)
- [Mechanisms for a No-Regret Agent: Beyond the Common Prior](https://mlsanity.com/paper/2009.05518/) (2020)
- [Safe Convex Learning under Uncertain Constraints](https://mlsanity.com/paper/1903.04626/) (2019)
- [Algorithmic Persuasion with No Externalities](https://mlsanity.com/paper/1609.06825/) (2016)
- [Prior-Independent Mechanisms for Scheduling](https://mlsanity.com/paper/1305.0597/) (2013)
- [Information Design in Spatial Resource Competition](https://mlsanity.com/paper/1909.12723/) (2019)
- [The Secretary Recommendation Problem](https://mlsanity.com/paper/1907.04252/) (2019)

## Built on by (most cited first, 12 of 12)

- [Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning](https://mlsanity.com/paper/2202.10678/) (2022)
- [No-Regret Learning in Bilateral Trade via Global Budget Balance](https://mlsanity.com/paper/2310.12370/) (2023)
- [Incentivizing Combinatorial Bandit Exploration](https://mlsanity.com/paper/2206.00494/) (2022)
- [Sequential Information Design: Learning to Persuade in the Dark](https://mlsanity.com/paper/2209.03927/) (2022)
- [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)
- [Persuading a Behavioral Agent: Approximately Best Responding and Learning](https://mlsanity.com/paper/2302.03719/) (2023)
- [Learning to Incentivize Information Acquisition: Proper Scoring Rules Meet Principal-Agent Model](https://mlsanity.com/paper/2303.08613/) (2023)
- [Generalized Principal-Agent Problem with a Learning Agent](https://mlsanity.com/paper/2402.09721/) (2024)
- [Algorithmic Persuasion Through Simulation](https://mlsanity.com/paper/2311.18138/) (2023)
- [On Incentivized Exploration beyond Bayesianism and Full-Information](https://mlsanity.com/paper/2607.18300/) (2026)
- [Learning to Price with Persuasion](https://mlsanity.com/paper/2608.16699/) (2026)

## Abstract (arXiv)

Motivated by information sharing in online platforms, we study repeated persuasion between a sender and a stream of receivers where at each time, the sender observes a payoff-relevant state drawn independently and identically from an unknown distribution, and shares state information with the receivers who each choose an action. The sender seeks to persuade the receivers into taking actions aligned with the sender's preference by selectively sharing state information. However, in contrast to the standard models, neither the sender nor the receivers know the distribution, and the sender has to persuade while learning the distribution on the fly. We study the sender's learning problem of making persuasive action recommendations to achieve low regret against the optimal persuasion mechanism with the knowledge of the distribution. To do this, we first propose and motivate a persuasiveness criterion for the unknown distribution setting that centers robustness as a requirement in the face of uncertainty. Our main result is an algorithm that, with high probability, is robustly-persuasive and achieves O(√Tlog T) regret, where T is the horizon length. Intuitively, at each time our algorithm maintains a set of candidate distributions, and chooses a signaling mechanism that is simultaneously persuasive for all of them. Core to our proof is a tight analysis about the cost of robust persuasion, which may be of independent interest. We further prove that this regret order is optimal (up to logarithmic terms) by showing that no algorithm can achieve regret better than Omega(√T).