# Learning in Bayesian Stackelberg Games With Unknown Follower's Types

arXiv: https://arxiv.org/abs/2602.00771 · HTML: https://mlsanity.com/paper/2602.00771/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 28 references that are in the map.
- First posted on arXiv 31 Jan 2026.

## Builds on (most cited first, 14 of 14)

- [Adaptive Contract Design for Crowdsourcing Markets: Bandit Algorithms for Repeated Principal-Agent Problems](https://mlsanity.com/paper/1405.2875/) (2014)
- [Sample-Efficient Learning of Stackelberg Equilibria in General-Sum Games](https://mlsanity.com/paper/2102.11494/) (2021)
- [The Sample Complexity of Online Contract Design](https://mlsanity.com/paper/2211.05732/) (2022)
- [Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning](https://mlsanity.com/paper/2202.10678/) (2022)
- [Optimal Rates and Efficient Algorithms for Online Bayesian Persuasion](https://mlsanity.com/paper/2303.01296/) (2023)
- [Learning Approximately Optimal Contracts](https://mlsanity.com/paper/1811.06736/) (2018)
- [No-Regret Learning in Dynamic Stackelberg Games](https://mlsanity.com/paper/2202.04786/) (2022)
- [Nearly-Optimal Bandit Learning in Stackelberg Games with Side Information](https://mlsanity.com/paper/2502.00204/) (2025)
- [Learning Optimal Contracts: How to Exploit Small Action Spaces](https://mlsanity.com/paper/2309.09801/) (2023)
- [Online Bayesian Persuasion Without a Clue](https://mlsanity.com/paper/2411.06141/) (2024)
- [The Sample Complexity of Stackelberg Games](https://mlsanity.com/paper/2405.06977/) (2024)
- [Information Design with Unknown Prior](https://mlsanity.com/paper/2410.05533/) (2024)
- [Learning in Structured Stackelberg Games](https://mlsanity.com/paper/2504.09006/) (2025)
- [Learning to Play Multi-Follower Bayesian Stackelberg Games](https://mlsanity.com/paper/2510.01387/) (2025)

## Built on by (most cited first, 2 of 2)

- [Learning to Persuade Privately Informed Receivers](https://mlsanity.com/paper/2607.28342/) (2026)
- [Learning Principal-Agent Contracts for Equitable Smallholder Carbon Farming under Moral Hazard and Adverse Selection](https://mlsanity.com/paper/2609.20404/) (2026)

## Abstract (arXiv)

We study online learning in Bayesian Stackelberg games, where a leader repeatedly interacts with a follower whose unknown private type is independently drawn at each round from an unknown probability distribution. The goal is to design algorithms that minimize the leader's regret with respect to always playing an optimal commitment computed with knowledge of the game. We consider, for the first time to the best of our knowledge, the most realistic case in which the leader does not know anything about the follower's types, i.e., the possible follower payoffs. This raises considerable additional challenges compared to the commonly studied case in which the payoffs of follower types are known. First, we prove a strong negative result: no-regret is unattainable under action feedback, i.e., when the leader only observes the follower's best response at the end of each round. Thus, we focus on the easier type feedback model, where the follower's type is also revealed. In such a setting, we propose a no-regret algorithm that achieves a regret of widetildeO(√T), when ignoring the dependence on other parameters.