Learning Constraints from Demonstrations
This work addresses the challenge of inferring constraints in robotics or control systems from limited demonstration data, which is incremental as it extends existing learning from demonstration methods.
The paper tackles the problem of learning unknown constraints shared across tasks from demonstrations, using safe and unsafe trajectories to obtain a consistent representation of the unsafe set via an integer program, and demonstrates it on linear and nonlinear dynamics with modifications for suboptimal demonstrations and feature space learning.
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. We also provide theoretical analysis on what subset of the constraint 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.