Abstraction-based branch and bound approach to Q-learning for hybrid optimal control

Benoît Legat, Raphaël M. Jungers, Jean Bouchat
Proceedings of the 3rd Conference on Learning for Dynamics and Control, PMLR 144:263-274, 2021.

Abstract

In this paper, we design a theoretical framework allowing to apply model predictive control on hybrid systems. For this, we develop a theory of approximate dynamic programming by leveraging the concept of alternating simulation. We show how to combine these notions in a branch and bound algorithm that can further refine the Q-functions using Lagrangian duality. We illustrate the approach on a numerical example.

Cite this Paper

BibTeX
@InProceedings{pmlr-v144-legat21a, title = {Abstraction-based branch and bound approach to {Q}-learning for hybrid optimal control}, author = {Legat, Beno\^it and Jungers, Rapha\"el M. and Bouchat, Jean}, booktitle = {Proceedings of the 3rd Conference on Learning for Dynamics and Control}, pages = {263--274}, year = {2021}, editor = {Jadbabaie, Ali and Lygeros, John and Pappas, George J. and A. Parrilo, Pablo and Recht, Benjamin and Tomlin, Claire J. and Zeilinger, Melanie N.}, volume = {144}, series = {Proceedings of Machine Learning Research}, month = {07 -- 08 June}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v144/legat21a/legat21a.pdf}, url = {https://proceedings.mlr.press/v144/legat21a.html}, abstract = {In this paper, we design a theoretical framework allowing to apply model predictive control on hybrid systems. For this, we develop a theory of approximate dynamic programming by leveraging the concept of alternating simulation. We show how to combine these notions in a branch and bound algorithm that can further refine the Q-functions using Lagrangian duality. We illustrate the approach on a numerical example.} }
Endnote
%0 Conference Paper %T Abstraction-based branch and bound approach to Q-learning for hybrid optimal control %A Benoît Legat %A Raphaël M. Jungers %A Jean Bouchat %B Proceedings of the 3rd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2021 %E Ali Jadbabaie %E John Lygeros %E George J. Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire J. Tomlin %E Melanie N. Zeilinger %F pmlr-v144-legat21a %I PMLR %P 263--274 %U https://proceedings.mlr.press/v144/legat21a.html %V 144 %X In this paper, we design a theoretical framework allowing to apply model predictive control on hybrid systems. For this, we develop a theory of approximate dynamic programming by leveraging the concept of alternating simulation. We show how to combine these notions in a branch and bound algorithm that can further refine the Q-functions using Lagrangian duality. We illustrate the approach on a numerical example.
APA
Legat, B., Jungers, R.M. & Bouchat, J.. (2021). Abstraction-based branch and bound approach to Q-learning for hybrid optimal control. Proceedings of the 3rd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 144:263-274 Available from https://proceedings.mlr.press/v144/legat21a.html.

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