Iterative Linearized Control: Stable Algorithms and Complexity Guarantees

Vincent Roulet, Siddhartha Srinivasa, Dmitriy Drusvyatskiy, Zaid Harchaoui
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:5518-5527, 2019.

Abstract

We examine popular gradient-based algorithms for nonlinear control in the light of the modern complexity analysis of first-order optimization algorithms. The examination reveals that the complexity bounds can be clearly stated in terms of calls to a computational oracle related to dynamic programming and implementable by gradient back-propagation using machine learning software libraries such as PyTorch or TensorFlow. Finally, we propose a regularized Gauss-Newton algorithm enjoying worst-case complexity bounds and improved convergence behavior in practice. The software library based on PyTorch is publicly available.

Cite this Paper

BibTeX
@InProceedings{pmlr-v97-roulet19a, title = {Iterative Linearized Control: Stable Algorithms and Complexity Guarantees}, author = {Roulet, Vincent and Srinivasa, Siddhartha and Drusvyatskiy, Dmitriy and Harchaoui, Zaid}, booktitle = {Proceedings of the 36th International Conference on Machine Learning}, pages = {5518--5527}, year = {2019}, editor = {Chaudhuri, Kamalika and Salakhutdinov, Ruslan}, volume = {97}, series = {Proceedings of Machine Learning Research}, month = {09--15 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v97/roulet19a/roulet19a.pdf}, url = {https://proceedings.mlr.press/v97/roulet19a.html}, abstract = {We examine popular gradient-based algorithms for nonlinear control in the light of the modern complexity analysis of first-order optimization algorithms. The examination reveals that the complexity bounds can be clearly stated in terms of calls to a computational oracle related to dynamic programming and implementable by gradient back-propagation using machine learning software libraries such as PyTorch or TensorFlow. Finally, we propose a regularized Gauss-Newton algorithm enjoying worst-case complexity bounds and improved convergence behavior in practice. The software library based on PyTorch is publicly available.} }
Endnote
%0 Conference Paper %T Iterative Linearized Control: Stable Algorithms and Complexity Guarantees %A Vincent Roulet %A Siddhartha Srinivasa %A Dmitriy Drusvyatskiy %A Zaid Harchaoui %B Proceedings of the 36th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2019 %E Kamalika Chaudhuri %E Ruslan Salakhutdinov %F pmlr-v97-roulet19a %I PMLR %P 5518--5527 %U https://proceedings.mlr.press/v97/roulet19a.html %V 97 %X We examine popular gradient-based algorithms for nonlinear control in the light of the modern complexity analysis of first-order optimization algorithms. The examination reveals that the complexity bounds can be clearly stated in terms of calls to a computational oracle related to dynamic programming and implementable by gradient back-propagation using machine learning software libraries such as PyTorch or TensorFlow. Finally, we propose a regularized Gauss-Newton algorithm enjoying worst-case complexity bounds and improved convergence behavior in practice. The software library based on PyTorch is publicly available.
APA
Roulet, V., Srinivasa, S., Drusvyatskiy, D. & Harchaoui, Z.. (2019). Iterative Linearized Control: Stable Algorithms and Complexity Guarantees. Proceedings of the 36th International Conference on Machine Learning, in Proceedings of Machine Learning Research 97:5518-5527 Available from https://proceedings.mlr.press/v97/roulet19a.html.

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