Learning Density Distribution of Reachable States for Autonomous Systems

Yue Meng, Dawei Sun, Zeng Qiu, Md Tawhid Bin Waez, Chuchu Fan
Proceedings of the 5th Conference on Robot Learning, PMLR 164:124-136, 2022.

Abstract

State density distribution, in contrast to worst-case reachability, can be leveraged for safety-related problems to better quantify the likelihood of the risk for potentially hazardous situations. In this work, we propose a data-driven method to compute the density distribution of reachable states for nonlinear and even black-box systems. Our semi-supervised approach learns system dynamics and the state density jointly from trajectory data, guided by the fact that the state density evolution follows the Liouville partial differential equation. With the help of neural network reachability tools, our approach can estimate the set of all possible future states as well as their density. Moreover, we could perform online safety verification with probability ranges for unsafe behaviors to occur. We use an extensive set of experiments to show that our learned solution can produce a much more accurate estimate on density distribution, and can quantify risks less conservatively and flexibly comparing with worst-case analysis.

Cite this Paper

BibTeX
@InProceedings{pmlr-v164-meng22a, title = {Learning Density Distribution of Reachable States for Autonomous Systems}, author = {Meng, Yue and Sun, Dawei and Qiu, Zeng and Waez, Md Tawhid Bin and Fan, Chuchu}, booktitle = {Proceedings of the 5th Conference on Robot Learning}, pages = {124--136}, year = {2022}, editor = {Faust, Aleksandra and Hsu, David and Neumann, Gerhard}, volume = {164}, series = {Proceedings of Machine Learning Research}, month = {08--11 Nov}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v164/meng22a/meng22a.pdf}, url = {https://proceedings.mlr.press/v164/meng22a.html}, abstract = {State density distribution, in contrast to worst-case reachability, can be leveraged for safety-related problems to better quantify the likelihood of the risk for potentially hazardous situations. In this work, we propose a data-driven method to compute the density distribution of reachable states for nonlinear and even black-box systems. Our semi-supervised approach learns system dynamics and the state density jointly from trajectory data, guided by the fact that the state density evolution follows the Liouville partial differential equation. With the help of neural network reachability tools, our approach can estimate the set of all possible future states as well as their density. Moreover, we could perform online safety verification with probability ranges for unsafe behaviors to occur. We use an extensive set of experiments to show that our learned solution can produce a much more accurate estimate on density distribution, and can quantify risks less conservatively and flexibly comparing with worst-case analysis.} }
Endnote
%0 Conference Paper %T Learning Density Distribution of Reachable States for Autonomous Systems %A Yue Meng %A Dawei Sun %A Zeng Qiu %A Md Tawhid Bin Waez %A Chuchu Fan %B Proceedings of the 5th Conference on Robot Learning %C Proceedings of Machine Learning Research %D 2022 %E Aleksandra Faust %E David Hsu %E Gerhard Neumann %F pmlr-v164-meng22a %I PMLR %P 124--136 %U https://proceedings.mlr.press/v164/meng22a.html %V 164 %X State density distribution, in contrast to worst-case reachability, can be leveraged for safety-related problems to better quantify the likelihood of the risk for potentially hazardous situations. In this work, we propose a data-driven method to compute the density distribution of reachable states for nonlinear and even black-box systems. Our semi-supervised approach learns system dynamics and the state density jointly from trajectory data, guided by the fact that the state density evolution follows the Liouville partial differential equation. With the help of neural network reachability tools, our approach can estimate the set of all possible future states as well as their density. Moreover, we could perform online safety verification with probability ranges for unsafe behaviors to occur. We use an extensive set of experiments to show that our learned solution can produce a much more accurate estimate on density distribution, and can quantify risks less conservatively and flexibly comparing with worst-case analysis.
APA
Meng, Y., Sun, D., Qiu, Z., Waez, M.T.B. & Fan, C.. (2022). Learning Density Distribution of Reachable States for Autonomous Systems. Proceedings of the 5th Conference on Robot Learning, in Proceedings of Machine Learning Research 164:124-136 Available from https://proceedings.mlr.press/v164/meng22a.html.

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