Adaptive Teaching of Temporal Logic Formulas to Learners with Preferences

• URL: http://arxiv.org/abs/2001.09956v1
• Date: Mon, 27 Jan 2020 18:22:53 GMT
• Title: Adaptive Teaching of Temporal Logic Formulas to Learners with Preferences
• Authors: Zhe Xu, Yuxin Chen and Ufuk Topcu
• Abstract summary: We investigate machine teaching for temporal logic formulas. An exhaustive search even for a myopic solution takes exponential time. We propose an efficient approach for teaching parametric linear temporal logic formulas.
• Score: 44.63937003271641
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Machine teaching is an algorithmic framework for teaching a target hypothesis via a sequence of examples or demonstrations. We investigate machine teaching for temporal logic formulas -- a novel and expressive hypothesis class amenable to time-related task specifications. In the context of teaching temporal logic formulas, an exhaustive search even for a myopic solution takes exponential time (with respect to the time span of the task). We propose an efficient approach for teaching parametric linear temporal logic formulas. Concretely, we derive a necessary condition for the minimal time length of a demonstration to eliminate a set of hypotheses. Utilizing this condition, we propose a myopic teaching algorithm by solving a sequence of integer programming problems. We further show that, under two notions of teaching complexity, the proposed algorithm has near-optimal performance. The results strictly generalize the previous results on teaching preference-based version space learners. We evaluate our algorithm extensively under a variety of learner types (i.e., learners with different preference models) and interactive protocols (e.g., batched and adaptive). The results show that the proposed algorithms can efficiently teach a given target temporal logic formula under various settings, and that there are significant gains of teaching efficacy when the teacher adapts to the learner's current hypotheses or uses oracles.

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