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

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Glen Chou , Necmiye Özay , Dmitry Berenson ·

YOU? · · 2020 · Open Access · · DOI: https://doi.org/10.48550/arxiv.2006.02411

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.

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Karush–Kuhn–Tucker conditions Counterexample Proposition Completeness (order theory) Function (biology) Linear temporal logic Mathematics Temporal logic Computer science Theoretical computer science Artificial intelligence Discrete mathematics Mathematical optimization Biology Epistemology Philosophy Evolutionary biology Mathematical analysis

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Type: preprint
Language: en
Landing Page: http://arxiv.org/abs/2006.02411
PDF: https://arxiv.org/pdf/2006.02411
OA Status: green
Cited By: 2
References: 39
Related Works: 10
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DOI: https://doi.org/10.48550/arxiv.2006.02411

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

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Language: en

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Publication year: 2020

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Publication date: 2020-06-03

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Authors: Glen Chou, Necmiye Özay, Dmitry Berenson

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Concepts: Karush–Kuhn–Tucker conditions, Counterexample, Proposition, Completeness (order theory), Function (biology), Linear temporal logic, Mathematics, Temporal logic, Computer science, Theoretical computer science, Artificial intelligence, Discrete mathematics, Mathematical optimization, Biology, Epistemology, Philosophy, Evolutionary biology, Mathematical analysis

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Cited by: 2

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