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arXiv · 2010.10012

Preference-Based Batch and Sequential Teaching

Farnam Mansouri·Yuxin Chen·Ara Vartanian·Xiaojin Zhu·Adish Singla
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Abstract

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 $Σ$. In our framework, each function $σ\in Σ$ induces a teacher-learner pair with teaching complexity as $TD(σ)$. 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 $TD(σ)$ associated with different families of the preference functions, e.g., comparison to the VC dimension of the hypothesis class and additivity/sub-additivity of $TD(σ)$ 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.

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BibTeXRIS

Farnam Mansouri, Yuxin Chen, Ara Vartanian, Xiaojin Zhu, Adish Singla. 2020-10-17. Preference-Based Batch and Sequential Teaching. https://arxiv.org/abs/2010.10012

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