We extend the learning from demonstration paradigm by providing a method for learning unknown constraints shared across tasks, using demonstrations of the tasks, their cost functions, and knowledge of the system dynamics and control constraints. Given safe demonstrations, our method uses hit-and-run sampling to obtain lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a consistent representation of the unsafe set via solving an integer program. Our method generalizes across system dynamics and learns a guaranteed subset of the constraint. In addition, by leveraging a known parameterization of the constraint, we modify our method to learn parametric constraints in high dimensions. We also provide theoretical analysis on what subset of the constraint and safe set can be learnable from safe demonstrations. We demonstrate our method on linear and nonlinear system dynamics, show that it can be modified to work with suboptimal demonstrations, and that it can also be used to learn constraints in a feature space.

我们通过提供一种学习跨任务共享的未知约束的方法，使用任务的演示、它们的成本函数以及系统动力学和控制约束的知识来扩展从演示范式的学习。鉴于安全演示，我们的方法使用命中和运行采样来获得较低的成本，因此不安全的轨迹。安全和不安全轨迹都用于通过求解整数程序来获得不安全集的一致表示。我们的方法概括了系统动力学并学习了有保证的约束子集。此外，通过利用约束的已知参数化，我们修改了我们的方法以学习高维参数化约束。我们还提供了关于约束和安全集的哪些子集可以从安全演示中学习的理论分析。