Learning Constraints from Locally-Optimal Demonstrations under Cost Function Uncertainty
This addresses the challenge of inferring constraints from demonstrations for robotics and autonomous systems, but it is incremental as it builds on existing constraint-learning approaches with specific enhancements.
The paper tackles the problem of learning parametric constraints from locally-optimal demonstrations when the cost function is uncertain, using KKT conditions and MILP to recover constraints with theoretical guarantees on conservativeness. It demonstrates improved performance over competing methods in high-dimensional systems like 7-DOF arms and quadrotors, enabling new constraint-satisfying trajectories.
We present an algorithm for learning parametric constraints from locally-optimal demonstrations, where the cost function being optimized is uncertain to the learner. Our method uses the Karush-Kuhn-Tucker (KKT) optimality conditions of the demonstrations within a mixed integer linear program (MILP) to learn constraints which are consistent with the local optimality of the demonstrations, by either using a known constraint parameterization or by incrementally growing a parameterization that is consistent with the demonstrations. We provide theoretical guarantees on the conservativeness of the recovered safe/unsafe sets and analyze the limits of constraint learnability when using locally-optimal demonstrations. We evaluate our method on high-dimensional constraints and systems by learning constraints for 7-DOF arm and quadrotor examples, show that it outperforms competing constraint-learning approaches, and can be effectively used to plan new constraint-satisfying trajectories in the environment.