Learning Parametric Constraints in High Dimensions from Demonstrations
This addresses the challenge of constraint recovery for high-dimensional systems, which is incremental as it builds on existing methods with theoretical guarantees.
The paper tackles the problem of learning parametric constraints in high dimensions from safe expert demonstrations by using hit-and-run sampling to generate unsafe trajectories and solving an integer program, and shows that it outperforms baseline approaches on high-dimensional systems like a 7-DOF arm, quadrotor, and planar pushing examples.
We present a scalable algorithm for learning parametric constraints in high dimensions from safe expert demonstrations. To reduce the ill-posedness of the constraint recovery problem, our method uses hit-and-run sampling to generate lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a representation of the unsafe set that is compatible with the data by solving an integer program in that representation's parameter space. Our method can either leverage a known parameterization or incrementally grow a parameterization while remaining consistent with the data, and we provide theoretical guarantees on the conservativeness of the recovered unsafe set. We evaluate our method on high-dimensional constraints for high-dimensional systems by learning constraints for 7-DOF arm, quadrotor, and planar pushing examples, and show that our method outperforms baseline approaches.