Learning to Incentivize Information Acquisition: Proper Scoring Rules Meet Principal-Agent Model
This addresses the challenge of designing optimal scoring rules for strategic information acquisition, which is incremental as it adapts existing methods to a specific model.
The paper tackles the problem of incentivizing an agent to acquire information for a principal in an online setting, achieving a sublinear T^{2/3}-regret after T iterations with an algorithm based on UCB.
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.