A brief note on learning problem with global perspectives
Getachew K. Befekadu
TL;DR
The paper tackles learning in a dynamic principal-agent setting where agents possess global perspectives on the learning process and the principal guides aggregation through an empirical-likelihood objective under conditional moment restrictions. It introduces a two-tier approach: (i) a gradient-based, distributed parameter updating scheme for agents with aggregation via a stochastic matrix, and (ii) a kernel-smoothed, constrained empirical-likelihood optimization for the principal that uses out-of-sample performance and privately held data to shape the aggregation. A concrete algorithm alternates between solving for Lagrange multipliers and a β-parameter to obtain favorable weights, followed by updating aggregated parameters and repeating until convergence. The framework aims to yield stability and consistency in collaborative learning with distributed/private data, though it notes unresolved issues such as small-sample properties and other theoretical challenges.
Abstract
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.