Analysis of on-line learning when a moving teacher goes around a true   teacher
  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 or due to noises. The generalization performance of a new student supervised by a moving machine has been analyzed. A model composed of a true teacher, a moving teacher and a student that are all linear perceptrons with noises has been treated analytically using statistical mechanics. It has been proven that the generalization errors of a student can be smaller than that of a moving teacher, even if the student only uses examples from the moving teacher. 
Seiji Miyoshi and Masato Okada