Learning Constraints from Locally-Optimal Demonstrations under Cost Function Uncertainty

• URL: http://arxiv.org/abs/2001.09336v1
• Date: Sat, 25 Jan 2020 15:57:48 GMT
• Title: Learning Constraints from Locally-Optimal Demonstrations under Cost Function Uncertainty
• Authors: Glen Chou, Necmiye Ozay, Dmitry Berenson
• Abstract summary: 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. 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
• Score: 6.950510860295866
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

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