Iterative Classroom Teaching

Abstract

We consider the machine teaching problem in a classroom-like setting wherein the teacher has to deliver the same examples to a diverse group of students. Their diversity stems from differences in their initial internal states as well as their learning rates. We prove that a teacher with full knowledge about the learning dynamics of the students can teach a target concept to the entire classroom using O min {d, N } log 1 examples, where d is the ambient dimension of the problem, N is the number of learners, and is the accuracy parameter. We show the robustness of our teaching strategy when the teacher has limited knowledge of the learners' internal dynamics as provided by a noisy oracle. Further, we study the trade-off between the learners' workload and the teacher's cost in teaching the target concept. Our experiments validate our theoretical results and suggest that appropriately partitioning the classroom into homogenous groups provides a balance between these two objectives.

Teaching Multiple Inverse Reinforcement Learners

“…We identified a set of conditions that determine whether class teaching is possible or not. Contrary to several recent results for density estimation and supervised learning (Zhu et al, 2017;Yeo et al, 2019), where class teaching is always possible (even if with some added effort), in the case of IRL teaching, our results establish that class teaching is not always possible. We illustrated the main findings of our paper by comparing our proposed algorithms in several different simulation scenarios with natural baselines.…”

“…The same work also establishes that, by dividing a group of learners in small groups, it is possible to attain a smaller teaching dimension. Yeo et al ( 2019 ) generalize those results for more complex learning problems, and consider additional differences between the learners, e.g., learning rates. Teaching to multiple learners, in the context of classification tasks, has also been considered with more complex learning models, for example when each learner has an exponentially decayed memory (Zhou et al, 2018 ).…”

“…Teaching a sequential task in a class setting, however, poses several additional complications found neither in single-agent settings (Cakmak and Lopes, 2012 ; Walsh and Goschin, 2012 ; Haug et al, 2018 ; Brown and Niekum, 2019 ), nor on estimation/classification settings (Walsh and Goschin, 2012 ; Zhu et al, 2017 ; Yeo et al, 2019 ). In such setting, we need to teach not only one particular learner but a whole diverse group of learners.…”

“…As an example, in the family of tasks considered by Zhu et al ( 2017 ) or Yeo et al ( 2019 ), learners have large differences in their prior information. But, no matter how large this difference is, all learners can be taught with the same demonstration, even if a larger number of samples is required.…”

Class Teaching for Inverse Reinforcement Learners

“…Zhu et al [26] show that, by dividing a 1 INESC-ID, Instituto Superior Técnico, Portugal email: manuel.lopes@tecnico.ulisboa.pt 2 INESC-ID, Instituto Superior Técnico, Portugal email: fmelo@inesc-id.pt group of learners in small groups, it is possible to attain a smaller teaching dimension. The work of Yeo et al [23] generalize those results for more complex learning problems, and consider additional differences between the learners, e.g. learning rates.…”