While most supervised machine learning models assume that training examples are sampled at random or adversarially, this article is concerned with models of learning from a cooperative teacher that selects “helpful ” training examples. The number of training examples a learner needs for identifying a concept in a given class C of possible target concepts (sample complexity of C) is lower in models assuming such teachers, that is, “helpful ” examples can speed up the learning process. The problem of how a teacher and a learner can cooperate in order to reduce the sample complexity, yet without using “coding tricks”, has been widely addressed. Nevertheless, the resulting teaching and learning protocols do not seem to make the teacher select intuitively “helpful ” examples. The two models introduced in this paper are built on what we call subset teaching sets and recursive teaching sets. They extend previous models of teaching by letting both the teacher and the learner exploit knowing that the partner is cooperative. For this purpose, we introduce a new notion of “coding trick”/“collusion”. We show how both resulting sample complexity measures (the subset teaching dimension an
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