Statistical Mechanics of On-line Learning when a Moving Teacher Goes around an Unlearnable True Teacher

TL;DR

This paper uses statistical mechanics to analyze how a student learning from a moving teacher in online learning can temporarily outperform the teacher in generalization, but ultimately converges to the teacher's performance, revealing non-linear effects.

Contribution

It provides a theoretical analysis of the generalization performance of a student learning from a moving nonmonotonic perceptron teacher using statistical mechanics.

Findings

Student's generalization error can temporarily be smaller than the teacher's.

Eventually, the student's error converges to the teacher's error.

Behavior differs from linear model predictions.

Abstract

In the framework of on-line learning, a learning machine might move around a teacher due to the differences in structures or output functions between the teacher and the learning machine. In this paper we analyze the generalization performance of a new student supervised by a moving machine. A model composed of a fixed true teacher, a moving teacher, and a student is treated theoretically using statistical mechanics, where the true teacher is a nonmonotonic perceptron and the others are simple perceptrons. Calculating the generalization errors numerically, we show that the generalization errors of a student can temporarily become smaller than that of a moving teacher, even if the student only uses examples from the moving teacher. However, the generalization error of the student eventually becomes the same value with that of the moving teacher. This behavior is qualitatively different from that of a linear model.