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.