Learning temporal logic formulas from suboptimal demonstrations: theory and experiments

Glen Chou, Necmiye Ozay, Dmitry Berenson

Abstract: We present a method for learning multi-stage tasks from demonstrations by learning the logical structure and atomic propositions of a consistent linear temporal logic (LTL) formula. The learner is given successful but potentially suboptimal demonstrations, where the demonstrator is optimizing a cost function while satisfying the LTL formula, and the cost function is uncertain to the learner. Our algorithm uses the Karush-Kuhn-Tucker (KKT) optimality conditions of the demonstrations together with a counterexample-guided falsification strategy to learn the atomic proposition parameters and logical structure of the LTL formula, respectively. We provide theoretical guarantees on the conservativeness of the recovered atomic proposition sets, as well as completeness in the search for finding an LTL formula consistent with the demonstrations. We evaluate our method on high-dimensional nonlinear systems by learning LTL formulas explaining multi-stage tasks on a simulated 7-DOF arm and a quadrotor, and show that it outperforms competing methods for learning LTL formulas from positive examples. Finally, we demonstrate that our approach can learn a real-world multi-stage tabletop manipulation task on a physical 7-DOF Kuka iiwa arm.