A brief note on learning problem with global perspectives

This brief note considers the problem of learning with dynamic-optimizing principal-agent setting, in which the agents are allowed to have global perspectives about the learning process, i.e., the ability to view things according to their relative importances or in their true relations based-on some aggregated information shared by the principal. Whereas, the principal, which is exerting an influence on the learning process of the agents in the aggregation, is primarily tasked to solve a high-level optimization problem posed as an empirical-likelihood estimator under conditional moment restrictions model that also accounts information about the agents' predictive performances on out-of-samples as well as a set of private datasets available only to the principal. In particular, we present a coherent mathematical argument which is necessary for characterizing the learning process behind this abstract principal-agent learning framework, although we acknowledge that there are a few conceptual and theoretical issues still need to be addressed.