Algorithmic machine teaching studies the interaction between a teacher and a learner where the teacher selects labeled examples aiming at teaching a target hypothesis.

Algorithmic machine teaching studies the interaction between a teacher and a learner where the teacher selects labeled examples aiming at teaching a target hypothesis. In a quest to lower teaching complexity and to achieve more natural teacher-learner interactions, several teaching models and complexity measures have been proposed for both the batch settings (e.g., worst-case, recursive, preference-based, and non-clashing models) as well as the sequential settings (e.g., local preference-based model). To better understand the connections between these different batch and sequential models, we develop a novel framework which captures the teaching process via preference functions $\Sigma$. In our framework, each function $\sigma \in \Sigma$ induces a teacher-learner pair with teaching complexity as $\TD(\sigma)$. We show that the above-mentioned teaching models are equivalent to specific types/families of preference functions in our framework. This equivalence, in turn, allows us to study the differences between two important teaching models, namely $\sigma$ functions inducing the strongest batch (i.e., non-clashing) model and $\sigma$ functions inducing a weak sequential (i.e., local preference-based) model. Finally, we identify preference functions inducing a novel family of sequential models with teaching complexity linear in the VC dimension of the hypothesis class: this is in contrast to the best known complexity result for the batch models which is quadratic in the VC dimension.

In machine teaching, a concept is represented by (and inferred from) a small number of labeled examples. Various teaching models in the literature cast the interaction between teacher and learner in a way to obtain a small complexity (in terms of the number of examples required for teaching a concept) while obeying certain constraints that are meant to prevent unfair collusion between teacher and learner. In recent years, one major research goal has been to show interesting relationships between teaching complexity and the VC-dimension (VCD). So far, the only interesting relationship known from batch teaching settings is an upper bound quadratic in the VCD, on a parameter called recursive teaching dimension. The only known upper bound on teaching complexity that is linear in VCD was obtained in a model of teaching with sequences rather than batches.This paper is the first to provide an upper bound of VCD on a batch teaching complexity parameter. This parameter, called STDmin, is introduced here as a model of teaching that intuitively incorporates a notion of ``importance'' of an example for a concept. In designing the STDmin teaching model, we argue that the standard notion of collusion-freeness from the literature may be inadequate for certain applications; we hence propose three desirable properties of teaching complexity and demonstrate that they are satisfied by STDmin.

Algorithmic machine teaching studies the interaction between a teacher and a learner where the teacher selects labeled examples aiming at teaching a target hypothesis.

In machine teaching, a concept is represented by (and inferred from) a small number of labeled examples.

Algorithmic machine teaching studies the interaction between a teacher and a learner where the teacher selects labeled examples aiming at teaching a target hypothesis. In a quest to lower teaching complexity and to achieve more natural teacher-learner interactions, several teaching models and complexity measures have been proposed for both the batch settings (e.g., worst-case, recursive, preference-based, and non-clashing models) as well as the sequential settings (e.g., local preference-based model). To better understand the connections between these different batch and sequential models, we develop a novel framework which captures the teaching process via preference functions \Sigma . In our framework, each function \sigma \in \Sigma induces a teacher-learner pair with teaching complexity as \TD(\sigma) . We show that the above-mentioned teaching models are equivalent to specific types/families of preference functions in our framework.

In machine teaching, a concept is represented by (and inferred from) a small number of labeled examples. Various teaching models in the literature cast the interaction between teacher and learner in a way to obtain a small complexity (in terms of the number of examples required for teaching a concept) while obeying certain constraints that are meant to prevent unfair collusion between teacher and learner. In recent years, one major research goal has been to show interesting relationships between teaching complexity and the VC-dimension (VCD). So far, the only interesting relationship known from batch teaching settings is an upper bound quadratic in the VCD, on a parameter called recursive teaching dimension. The only known upper bound on teaching complexity that is linear in VCD was obtained in a model of teaching with sequences rather than batches.This paper is the first to provide an upper bound of VCD on a batch teaching complexity parameter.

Algorithmic machine teaching studies the interaction between a teacher and a learner where the teacher selects labeled examples aiming at teaching a target hypothesis. In a quest to lower teaching complexity and to achieve more natural teacher-learner interactions, several teaching models and complexity measures have been proposed for both the batch settings (e.g., worst-case, recursive, preference-based, and non-clashing models) as well as the sequential settings (e.g., local preference-based model). To better understand the connections between these different batch and sequential models, we develop a novel framework which captures the teaching process via preference functions \Sigma . In our framework, each function \sigma \in \Sigma induces a teacher-learner pair with teaching complexity as \TD(\sigma) . We show that the above-mentioned teaching models are equivalent to specific types/families of preference functions in our framework.

Algorithmic machine teaching studies the interaction between a teacher and a learner where the teacher selects labeled examples aiming at teaching a target hypothesis. In a quest to lower teaching complexity, several teaching models and complexity measures have been proposed for both the batch settings (e.g., worst-case, recursive, preference-based, and non-clashing models) and the sequential settings (e.g., local preference-based model). To better understand the connections between these models, we develop a novel framework that captures the teaching process via preference functions $\Sigma$. In our framework, each function $\sigma \in \Sigma$ induces a teacher-learner pair with teaching complexity as $TD(\sigma)$. We show that the above-mentioned teaching models are equivalent to specific types/families of preference functions. We analyze several properties of the teaching complexity parameter $TD(\sigma)$ associated with different families of the preference functions, e.g., comparison to the VC dimension of the hypothesis class and additivity/sub-additivity of $TD(\sigma)$ over disjoint domains. Finally, we identify preference functions inducing a novel family of sequential models with teaching complexity linear in the VC dimension: this is in contrast to the best-known complexity result for the batch models, which is quadratic in the VC dimension.