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We study the incentivized information acquisition problem, where a principalhires an agent to gather information on her behalf. Such a problem is modeledas a Stackelberg game between the principal and the agent, where the principalannounces a scoring rule that specifies the payment, and then the agent thenchooses an effort level that maximizes her own profit and reports theinformation. We study the online setting of such a problem from the principal'sperspective, i.e., designing the optimal scoring rule by repeatedly interactingwith the strategic agent. We design a provably sample efficient algorithm thattailors the UCB algorithm (Auer et al., 2002) to our model, which achieves asublinear $T^{2/3}$-regret after $T$ iterations. Our algorithm features adelicate estimation procedure for the optimal profit of the principal, and aconservative correction scheme that ensures the desired agent's actions areincentivized. Furthermore, a key feature of our regret bound is that it isindependent of the number of states of the environment.

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