  The contribution of this paper is a generalized formulation of correctional
learning using optimal transport, which is about how to optimally transport one
mass distribution to another. Correctional learning is a framework developed to
enhance the accuracy of parameter estimation processes by means of a
teacher-student approach. In this framework, an expert agent, referred to as
the teacher, modifies the data used by a learning agent, known as the student,
to improve its estimation process. The objective of the teacher is to alter the
data such that the student's estimation error is minimized, subject to a fixed
intervention budget. Compared to existing formulations of correctional
learning, our novel optimal transport approach provides several benefits. It
allows for the estimation of more complex characteristics as well as the
consideration of multiple intervention policies for the teacher. We evaluate
our approach on two theoretical examples, and on a human-robot interaction
application in which the teacher's role is to improve the robots performance in
an inverse reinforcement learning setting.
