Preference-Based Batch and Sequential Teaching

TL;DR

This paper introduces a unified framework for understanding various machine teaching models through preference functions, revealing new insights into teaching complexity and establishing connections between batch and sequential teaching paradigms.

Contribution

It develops a novel preference-based framework that unifies different teaching models and analyzes their complexity, highlighting a linear complexity family in sequential teaching.

Findings

Preference functions induce equivalent teaching models.

Teaching complexity relates to VC dimension and exhibits sub-additivity.

Sequential models can achieve linear complexity in VC dimension.

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 $\Sigma$. 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.