论文标题

对偏好的学习者的时间逻辑公式的自适应教学

Adaptive Teaching of Temporal Logic Formulas to Learners with Preferences

论文作者

Xu, Zhe, Chen, Yuxin, Topcu, Ufuk

论文摘要

机器教学是通过一系列示例或演示来教授目标假设的算法框架。我们研究了时间逻辑公式的机器教学 - 一种新颖而表达的假设类别,可符合时间相关的任务规范。在教授时间逻辑公式的背景下,即使是近视解决方案的详尽搜索也需要指数时间(关于任务的时间跨度)。我们提出了一种教学参数线性时间逻辑公式的有效方法。具体而言,我们得出了消除一组假设的演示时间长度的最小时间长度的必要条件。利用这种情况,我们通过解决一系列整数编程问题来提出一种近视教学算法。我们进一步表明,在教学复杂性的两个概念下,拟议的算法的性能几乎是最佳的。结果严格将先前的结果概括为教授基于偏好的版本空间学习者。我们在各种学习者类型(即具有不同偏好模型的学习者)和交互式协议(例如,批处理和自适应)中广泛评估算法。结果表明,所提出的算法可以在各种环境下有效地教授给定的目标时间逻辑公式,并且当教师适应学习者当前的假设或使用orac时,教学功效就有很大的成就。

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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