Explaining Multi-stage Tasks by Learning Temporal Logic Formulas from Suboptimal Demonstrations
This addresses the challenge of interpreting complex robotic tasks from demonstrations for robotics and AI applications, representing an incremental advance in learning LTL formulas.
The paper tackles the problem of learning multi-stage tasks from suboptimal demonstrations by inferring linear temporal logic (LTL) formulas, using KKT conditions and counterexample-guided falsification to learn logical structure and atomic propositions. It demonstrates improved performance over competing methods on 7-DOF arm and quadrotor systems, though specific numerical gains are not provided.
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 7-DOF arm and quadrotor systems and show that it outperforms competing methods for learning LTL formulas from positive examples.