  We present an approach to Intelligent Tutoring Systems which adaptively
personalizes sequences of learning activities to maximize skills acquired by
students, taking into account the limited time and motivational resources. At a
given point in time, the system proposes to the students the activity which
makes them progress faster. We introduce two algorithms that rely on the
empirical estimation of the learning progress, RiARiT that uses information
about the difficulty of each exercise and ZPDES that uses much less knowledge
about the problem.
  The system is based on the combination of three approaches. First, it
leverages recent models of intrinsically motivated learning by transposing them
to active teaching, relying on empirical estimation of learning progress
provided by specific activities to particular students. Second, it uses
state-of-the-art Multi-Arm Bandit (MAB) techniques to efficiently manage the
exploration/exploitation challenge of this optimization process. Third, it
leverages expert knowledge to constrain and bootstrap initial exploration of
the MAB, while requiring only coarse guidance information of the expert and
allowing the system to deal with didactic gaps in its knowledge. The system is
evaluated in a scenario where 7-8 year old schoolchildren learn how to
decompose numbers while manipulating money. Systematic experiments are
presented with simulated students, followed by results of a user study across a
population of 400 school children.
