Adaptive Teaching of Temporal Logic Formulas to Learners with Preferences
share
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.
READ FULL TEXT