Lambda-Policy Iteration with Randomization for Contractive Models with Infinite Policies: Well-Posedness and Convergence

Yuchao Li, Karl Henrik Johansson, Jonas Mårtensson
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:540-549, 2020.

Abstract

Abstract dynamic programming models are used to analyze $\lambda$-policy iteration with randomization algorithms. Particularly, contractive models with infinite policies are considered and it is shown that well-posedness of the $\lambda$-operator plays a central role in the algorithm. The operator is known to be well-posed for problems with finite states, but our analysis shows that it is also well-defined for the contractive models with infinite states studied. Similarly, the algorithm we analyze is known to converge for problems with finite policies, but we identify the conditions required to guarantee convergence with probability one when the policy space is infinite regardless of the number of states. Guided by the analysis, we exemplify a data-driven approximated implementation of the algorithm for estimation of optimal costs of constrained linear and nonlinear control problems. Numerical results indicate potentials of this method in practice.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-li20b, title = {Lambda-Policy Iteration with Randomization for Contractive Models with Infinite Policies: Well-Posedness and Convergence}, author = {Li, Yuchao and Johansson, Karl Henrik and M{\aa}rtensson, Jonas}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {540--549}, year = {2020}, editor = {Bayen, Alexandre M. and Jadbabaie, Ali and Pappas, George and Parrilo, Pablo A. and Recht, Benjamin and Tomlin, Claire and Zeilinger, Melanie}, volume = {120}, series = {Proceedings of Machine Learning Research}, month = {10--11 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v120/li20b/li20b.pdf}, url = {https://proceedings.mlr.press/v120/li20b.html}, abstract = {Abstract dynamic programming models are used to analyze $\lambda$-policy iteration with randomization algorithms. Particularly, contractive models with infinite policies are considered and it is shown that well-posedness of the $\lambda$-operator plays a central role in the algorithm. The operator is known to be well-posed for problems with finite states, but our analysis shows that it is also well-defined for the contractive models with infinite states studied. Similarly, the algorithm we analyze is known to converge for problems with finite policies, but we identify the conditions required to guarantee convergence with probability one when the policy space is infinite regardless of the number of states. Guided by the analysis, we exemplify a data-driven approximated implementation of the algorithm for estimation of optimal costs of constrained linear and nonlinear control problems. Numerical results indicate potentials of this method in practice. } }
Endnote
%0 Conference Paper %T Lambda-Policy Iteration with Randomization for Contractive Models with Infinite Policies: Well-Posedness and Convergence %A Yuchao Li %A Karl Henrik Johansson %A Jonas Mårtensson %B Proceedings of the 2nd Conference on Learning for Dynamics and Control %C Proceedings of Machine Learning Research %D 2020 %E Alexandre M. Bayen %E Ali Jadbabaie %E George Pappas %E Pablo A. Parrilo %E Benjamin Recht %E Claire Tomlin %E Melanie Zeilinger %F pmlr-v120-li20b %I PMLR %P 540--549 %U https://proceedings.mlr.press/v120/li20b.html %V 120 %X Abstract dynamic programming models are used to analyze $\lambda$-policy iteration with randomization algorithms. Particularly, contractive models with infinite policies are considered and it is shown that well-posedness of the $\lambda$-operator plays a central role in the algorithm. The operator is known to be well-posed for problems with finite states, but our analysis shows that it is also well-defined for the contractive models with infinite states studied. Similarly, the algorithm we analyze is known to converge for problems with finite policies, but we identify the conditions required to guarantee convergence with probability one when the policy space is infinite regardless of the number of states. Guided by the analysis, we exemplify a data-driven approximated implementation of the algorithm for estimation of optimal costs of constrained linear and nonlinear control problems. Numerical results indicate potentials of this method in practice.
APA
Li, Y., Johansson, K.H. & Mårtensson, J.. (2020). Lambda-Policy Iteration with Randomization for Contractive Models with Infinite Policies: Well-Posedness and Convergence. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:540-549 Available from https://proceedings.mlr.press/v120/li20b.html.

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