Data-Driven Chance Constrained Control using Kernel Distribution Embeddings

Adam Thorpe, Thomas Lew, Meeko Oishi, Marco Pavone
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:790-802, 2022.

Abstract

We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows representing expectation operators as inner products in a reproducing kernel Hilbert space. This framework enables approximately reformulating the original problem using a dataset of observed trajectories from the system without imposing prior assumptions on the parameterization of the system dynamics or the structure of the uncertainty. By optimizing over a finite subset of stochastic open-loop control trajectories, we relax the original problem to a linear program over the control parameters that can be efficiently solved using standard convex optimization techniques. We demonstrate our proposed approach in simulation on a system with nonlinear non-Markovian dynamics navigating in a cluttered environment.

Cite this Paper


BibTeX
@InProceedings{pmlr-v168-thorpe22a, title = {Data-Driven Chance Constrained Control using Kernel Distribution Embeddings}, author = {Thorpe, Adam and Lew, Thomas and Oishi, Meeko and Pavone, Marco}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {790--802}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/thorpe22a/thorpe22a.pdf}, url = {https://proceedings.mlr.press/v168/thorpe22a.html}, abstract = {We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows representing expectation operators as inner products in a reproducing kernel Hilbert space. This framework enables approximately reformulating the original problem using a dataset of observed trajectories from the system without imposing prior assumptions on the parameterization of the system dynamics or the structure of the uncertainty. By optimizing over a finite subset of stochastic open-loop control trajectories, we relax the original problem to a linear program over the control parameters that can be efficiently solved using standard convex optimization techniques. We demonstrate our proposed approach in simulation on a system with nonlinear non-Markovian dynamics navigating in a cluttered environment.} }
Endnote
%0 Conference Paper %T Data-Driven Chance Constrained Control using Kernel Distribution Embeddings %A Adam Thorpe %A Thomas Lew %A Meeko Oishi %A Marco Pavone %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-thorpe22a %I PMLR %P 790--802 %U https://proceedings.mlr.press/v168/thorpe22a.html %V 168 %X We present a data-driven algorithm for efficiently computing stochastic control policies for general joint chance constrained optimal control problems. Our approach leverages the theory of kernel distribution embeddings, which allows representing expectation operators as inner products in a reproducing kernel Hilbert space. This framework enables approximately reformulating the original problem using a dataset of observed trajectories from the system without imposing prior assumptions on the parameterization of the system dynamics or the structure of the uncertainty. By optimizing over a finite subset of stochastic open-loop control trajectories, we relax the original problem to a linear program over the control parameters that can be efficiently solved using standard convex optimization techniques. We demonstrate our proposed approach in simulation on a system with nonlinear non-Markovian dynamics navigating in a cluttered environment.
APA
Thorpe, A., Lew, T., Oishi, M. & Pavone, M.. (2022). Data-Driven Chance Constrained Control using Kernel Distribution Embeddings. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:790-802 Available from https://proceedings.mlr.press/v168/thorpe22a.html.

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