Heuristic search of optimal machine teaching curricula

In curriculum learning the order of concepts is determined by the teacher but not the examples for each concept, while in machine teaching it is the examples that are chosen by the teacher to minimise the learning effort, though the concepts are taught in isolation. Curriculum teaching is the natural combination of both, where both concept order and the set of examples can be chosen to minimise the size of the whole teaching session. Yet, this simultaneous minimisation of teaching sets and concept order is computationally challenging, facing issues such as the “interposition” phenomenon: previous knowledge may be counter-productive. We build on a machine-teaching framework based on simplicity priors that can achieve short teaching sizes for large classes of languages. Given a set of concepts, we identify an inequality relating the sizes of example sets and concept descriptions. This leverages the definition of admissible heuristics for A* search to spot the optimal curricula by avoiding interposition, being able to find the shortest teaching sessions in a more efficient way than an exhaustive search and with the guarantees we do not have with a greedy algorithm. We illustrate these theoretical findings through case studies in a drawing domain, polygonal strokes on a grid described by a simple language implementing compositionality and recursion.