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

Author

Listed:
  • Siyu Chen
  • Jibang Wu
  • Yifan Wu
  • Zhuoran Yang

Abstract

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 $T^{2/3}$-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.

Suggested Citation

  • Siyu Chen & Jibang Wu & Yifan Wu & Zhuoran Yang, 2023. "Learning to Incentivize Information Acquisition: Proper Scoring Rules Meet Principal-Agent Model," Papers 2303.08613, arXiv.org, revised Aug 2023.
    • Handle: RePEc:arx:papers:2303.08613
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    References listed on IDEAS

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    1. Myerson, Roger B, 1979. "Incentive Compatibility and the Bargaining Problem," Econometrica, Econometric Society, vol. 47(1), pages 61-73, January.
    2. Jibang Wu & Zixuan Zhang & Zhe Feng & Zhaoran Wang & Zhuoran Yang & Michael I. Jordan & Haifeng Xu, 2022. "Sequential Information Design: Markov Persuasion Process and Its Efficient Reinforcement Learning," Papers 2202.10678, arXiv.org.
    3. Modibo Camara & Jason Hartline & Aleck Johnsen, 2020. "Mechanisms for a No-Regret Agent: Beyond the Common Prior," Papers 2009.05518, arXiv.org.
    4. Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
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