On-line Learning of an Unlearnable True Teacher through Mobile Ensemble Teachers

TL;DR

This paper investigates how a student perceptron can learn effectively from ensemble teachers that themselves learn from an unlearnable true teacher, using statistical mechanics to analyze transient and steady-state behaviors.

Contribution

It introduces a hierarchical online learning model where ensemble teachers learn from an unlearnable true teacher, revealing the benefits of dynamic ensemble teachers for student performance.

Findings

Student outperforms ensemble teachers in transient state

Moving ensemble teachers improves student learning efficiency

Ensemble teachers orbit around the true teacher maintaining fixed distance

Abstract

On-line learning of a hierarchical learning model is studied by a method from statistical mechanics. In our model a student of a simple perceptron learns from not a true teacher directly, but ensemble teachers who learn from the true teacher with a perceptron learning rule. Since the true teacher and the ensemble teachers are expressed as non-monotonic perceptron and simple ones, respectively, the ensemble teachers go around the unlearnable true teacher with the distance between them fixed in an asymptotic steady state. The generalization performance of the student is shown to exceed that of the ensemble teachers in a transient state, as was shown in similar ensemble-teachers models. Further, it is found that moving the ensemble teachers even in the steady state, in contrast to the fixed ensemble teachers, is efficient for the performance of the student.