Provably Efficient Algorithm for Best Scoring Rule Identification in Online Principal-Agent Information Acquisition

We investigate the problem of identifying the optimal scoring rule within the principal-agent framework for online information acquisition problem. We focus on the principal's perspective, seeking to determine the desired scoring rule through interactions with the agent. To address this challenge, we propose two algorithms: OIAFC and OIAFB, tailored for fixed confidence and fixed budget settings, respectively. Our theoretical analysis demonstrates that OIAFC can extract the desired $(\epsilon, \delta)$-scoring rule with a efficient instance-dependent sample complexity or an instance-independent sample complexity. Our analysis also shows that OIAFB matches the instance-independent performance bound of OIAFC, while both algorithms share the same complexity across fixed confidence and fixed budget settings.

We study how a manager (the principal) can figure out the best way to reward a worker (the agent) for collecting useful information over time. This is important in situations where the manager can't directly see the worker's effort but still wants to encourage honest and high-quality work. To solve this, we design two algorithms—OIAFC and OIAFB—that help the manager learn the best reward strategy. One works when the manager wants to be very confident in the result (fixed confidence), and the other works when there is a limited budget (fixed budget). Our analysis shows that both algorithms are efficient, and even though they work in different settings, they perform equally well in terms of how much data they need to make good decisions.