# Learning to Incentivize Information Acquisition: Proper Scoring Rules Meet Principal-Agent Model

arXiv: https://arxiv.org/abs/2303.08613 · HTML: https://mlsanity.com/paper/2303.08613/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 22 of its 55 references that are in the map.
- First posted on arXiv 15 Mar 2023.

## Builds on (most cited first, 22 of 22)

- [Is Q-learning Provably Efficient?](https://mlsanity.com/paper/1807.03765/) (2018)
- [Learning Prices for Repeated Auctions with Strategic Buyers](https://mlsanity.com/paper/1311.6838/) (2013)
- [The Sample Complexity of Online Contract Design](https://mlsanity.com/paper/2211.05732/) (2022)
- [Learning to Bid Without Knowing your Value](https://mlsanity.com/paper/1711.01333/) (2017)
- [Dynamic Incentive-aware Learning: Robust Pricing in Contextual Auctions](https://mlsanity.com/paper/2002.11137/) (2020)
- [Learning Equilibria in Matching Markets from Bandit Feedback](https://mlsanity.com/paper/2108.08843/) (2021)
- [Simple versus Optimal Contracts](https://mlsanity.com/paper/1808.03713/) (2018)
- [Learning in Stackelberg Games with Non-myopic Agents](https://mlsanity.com/paper/2208.09407/) (2022)
- [Optimization of Scoring Rules](https://mlsanity.com/paper/2007.02905/) (2020)
- [Contracts under Moral Hazard and Adverse Selection](https://mlsanity.com/paper/2010.06742/) (2020)
- [Mechanisms for a No-Regret Agent: Beyond the Common Prior](https://mlsanity.com/paper/2009.05518/) (2020)
- [Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning](https://mlsanity.com/paper/2202.10678/) (2022)
- [The Complexity of Contracts](https://mlsanity.com/paper/2002.12034/) (2020)
- [Binary Scoring Rules that Incentivize Precision](https://mlsanity.com/paper/2002.10669/) (2020)
- [Learning to Persuade on the Fly: Robustness Against Ignorance](https://mlsanity.com/paper/2102.10156/) (2021)
- [Bayesian Agency: Linear versus Tractable Contracts](https://mlsanity.com/paper/2106.00319/) (2021)
- [Contracts with Private Cost per Unit-of-Effort](https://mlsanity.com/paper/2111.09179/) (2021)
- [Optimal Scoring Rules for Multi-dimensional Effort](https://mlsanity.com/paper/2211.03302/) (2022)
- [On Stackelberg Mixed Strategies](https://mlsanity.com/paper/1705.07476/) (2017)
- [Designing Menus of Contracts Efficiently: The Power of Randomization](https://mlsanity.com/paper/2202.10966/) (2022)
- [Contracts with Information Acquisition, via Scoring Rules](https://mlsanity.com/paper/2204.01773/) (2022)
- [No-Regret Learning in Partially-Informed Auctions](https://mlsanity.com/paper/2202.10606/) (2022)

## Built on by (most cited first, 7 of 7)

- [Principal-Agent Reward Shaping in MDPs](https://mlsanity.com/paper/2401.00298/) (2023)
- [Learning to Mitigate Externalities: the Coase Theorem with Hindsight Rationality](https://mlsanity.com/paper/2406.19824/) (2024)
- [Aligned Textual Scoring Rules](https://mlsanity.com/paper/2507.06221/) (2025)
- [Learn then Decide: A Learning Approach for Designing Data Marketplaces](https://mlsanity.com/paper/2503.10773/) (2025)
- [No Bidding, No Regret: Pairwise-Feedback Mechanisms for Digital Goods and Data Auctions](https://mlsanity.com/paper/2306.01860/) (2023)
- [Provably Efficient Algorithm for Best Scoring Rule Identification in Online Principal-Agent Information Acquisition](https://mlsanity.com/paper/2505.17379/) (2025)
- [Scoring Rules! Statistical and Strategic Alignment for Text Evaluation Metrics](https://mlsanity.com/paper/2608.01423/) (2026)

## Abstract (arXiv)

We study the incentivized information acquisition problem, where a principal hires an agent to gather information on her behalf. Such a problem is modeled as a Stackelberg game between the principal and the agent, where the principal announces a scoring rule that specifies the payment, and then the agent then chooses an effort level that maximizes her own profit and reports the information. We study the online setting of such a problem from the principal's perspective, i.e., designing the optimal scoring rule by repeatedly interacting with the strategic agent. We design a provably sample efficient algorithm that tailors the UCB algorithm (Auer et al., 2002) to our model, which achieves a sublinear T2/3-regret after T iterations. Our algorithm features a delicate estimation procedure for the optimal profit of the principal, and a conservative correction scheme that ensures the desired agent's actions are incentivized. Furthermore, a key feature of our regret bound is that it is independent of the number of states of the environment.