  We consider a cooperative system identification scenario in which an expert
agent (teacher) knows a correct, or at least a good, model of the system and
aims to assist a learner-agent (student), but cannot directly transfer its
knowledge to the student. For example, the teacher's knowledge of the system
might be abstract or the teacher and student might be employing different model
classes, which renders the teacher's parameters uninformative to the student.
In this paper, we propose correctional learning as an approach to the above
problem: Suppose that in order to assist the student, the teacher can intercept
the observations collected from the system and modify them to maximize the
amount of information the student receives about the system. We formulate a
general solution as an optimization problem, which for a multinomial system
instantiates itself as an integer program. Furthermore, we obtain finite-sample
results on the improvement that the assistance from the teacher results in (as
measured by the reduction in the variance of the estimator) for a binomial
system.
