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Explaining Multi-stage Tasks by Learning Temporal Logic Formulas from Suboptimal Demonstrations

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Document pages: 16 pages

Abstract: We present a method for learning multi-stage tasks from demonstrations bylearning the logical structure and atomic propositions of a consistent lineartemporal logic (LTL) formula. The learner is given successful but potentiallysuboptimal demonstrations, where the demonstrator is optimizing a cost functionwhile satisfying the LTL formula, and the cost function is uncertain to thelearner. Our algorithm uses the Karush-Kuhn-Tucker (KKT) optimality conditionsof the demonstrations together with a counterexample-guided falsificationstrategy to learn the atomic proposition parameters and logical structure ofthe LTL formula, respectively. We provide theoretical guarantees on theconservativeness of the recovered atomic proposition sets, as well ascompleteness in the search for finding an LTL formula consistent with thedemonstrations. We evaluate our method on high-dimensional nonlinear systems bylearning LTL formulas explaining multi-stage tasks on 7-DOF arm and quadrotorsystems and show that it outperforms competing methods for learning LTLformulas from positive examples.

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