Teaching Multiple Inverse Reinforcement Learners

In this paper, we propose the first machine teaching algorithm for multiple inverse reinforcement learners. As our initial contribution, we formalize the problem of optimally teaching a sequential task to a heterogeneous class of learners. We then contribute a theoretical analysis of such problem, identifying conditions under which it is possible to conduct such teaching using the same demonstration for all learners. Our analysis shows that, contrary to other teaching problems, teaching a sequential task to a heterogeneous class of learners with a single demonstration may not be possible, as the differences between individual agents increase. We then contribute two algorithms that address the main difficulties identified by our theoretical analysis. The first algorithm, which we dub SplitTeach, starts by teaching the class as a whole until all students have learned all that they can learn as a group; it then teaches each student individually, ensuring that all students are able to perfectly acquire the target task. The second approach, which we dub JointTeach, selects a single demonstration to be provided to the whole class so that all students learn the target task as well as a single demonstration allows. While SplitTeach ensures optimal teaching at the cost of a bigger teaching effort, JointTeach ensures minimal effort, although the learners are not guaranteed to perfectly recover the target task. We conclude by illustrating our methods in several simulation domains. The simulation results agree with our theoretical findings, showcasing that indeed class teaching is not possible in the presence of heterogeneous students. At the same time, they also illustrate the main properties of our proposed algorithms: in all domains, SplitTeach guarantees perfect teaching and, in terms of teaching effort, is always at least as good as individualized teaching (often better); on the other hand, JointTeach attains minimal teaching effort in all domains, even if sometimes it compromises the teaching performance.