Learning Parametric Constraints in High Dimensions from Demonstrations

Glen Chou, Necmiye Ozay, Dmitry Berenson
Proceedings of the Conference on Robot Learning, PMLR 100:1211-1230, 2020.

Abstract

We present a scalable algorithm for learning parametric constraints in high dimensions from safe expert demonstrations. To reduce the ill-posedness of the constraint recovery problem, our method uses hit-and-run sampling to generate lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a representation of the unsafe set that is compatible with the data by solving an integer program in that representation’s parameter space. Our method can either leverage a known parameterization or incrementally grow a parameterization while remaining consistent with the data, and we provide theoretical guarantees on the conservativeness of the recovered unsafe set. We evaluate our method on high-dimensional constraints for high-dimensional systems by learning constraints for 7-DOF arm, quadrotor, and planar pushing examples, and show that our method outperforms baseline approaches.

Cite this Paper

BibTeX
@InProceedings{pmlr-v100-chou20a, title = {Learning Parametric Constraints in High Dimensions from Demonstrations}, author = {Chou, Glen and Ozay, Necmiye and Berenson, Dmitry}, booktitle = {Proceedings of the Conference on Robot Learning}, pages = {1211--1230}, year = {2020}, editor = {Kaelbling, Leslie Pack and Kragic, Danica and Sugiura, Komei}, volume = {100}, series = {Proceedings of Machine Learning Research}, month = {30 Oct--01 Nov}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v100/chou20a/chou20a.pdf}, url = {https://proceedings.mlr.press/v100/chou20a.html}, abstract = {We present a scalable algorithm for learning parametric constraints in high dimensions from safe expert demonstrations. To reduce the ill-posedness of the constraint recovery problem, our method uses hit-and-run sampling to generate lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a representation of the unsafe set that is compatible with the data by solving an integer program in that representation’s parameter space. Our method can either leverage a known parameterization or incrementally grow a parameterization while remaining consistent with the data, and we provide theoretical guarantees on the conservativeness of the recovered unsafe set. We evaluate our method on high-dimensional constraints for high-dimensional systems by learning constraints for 7-DOF arm, quadrotor, and planar pushing examples, and show that our method outperforms baseline approaches.} }
Endnote
%0 Conference Paper %T Learning Parametric Constraints in High Dimensions from Demonstrations %A Glen Chou %A Necmiye Ozay %A Dmitry Berenson %B Proceedings of the Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2020 %E Leslie Pack Kaelbling %E Danica Kragic %E Komei Sugiura %F pmlr-v100-chou20a %I PMLR %P 1211--1230 %U https://proceedings.mlr.press/v100/chou20a.html %V 100 %X We present a scalable algorithm for learning parametric constraints in high dimensions from safe expert demonstrations. To reduce the ill-posedness of the constraint recovery problem, our method uses hit-and-run sampling to generate lower cost, and thus unsafe, trajectories. Both safe and unsafe trajectories are used to obtain a representation of the unsafe set that is compatible with the data by solving an integer program in that representation’s parameter space. Our method can either leverage a known parameterization or incrementally grow a parameterization while remaining consistent with the data, and we provide theoretical guarantees on the conservativeness of the recovered unsafe set. We evaluate our method on high-dimensional constraints for high-dimensional systems by learning constraints for 7-DOF arm, quadrotor, and planar pushing examples, and show that our method outperforms baseline approaches.
APA
Chou, G., Ozay, N. & Berenson, D.. (2020). Learning Parametric Constraints in High Dimensions from Demonstrations. Proceedings of the Conference on Robot Learning, in Proceedings of Machine Learning Research 100:1211-1230 Available from https://proceedings.mlr.press/v100/chou20a.html.

Related Material