A Kernel Mean Embedding Approach to Reducing Conservativeness in Stochastic Programming and Control

Jia-Jie Zhu, Bernhard Schoelkopf, Moritz Diehl
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:915-923, 2020.

Abstract

In this paper, we apply kernel mean embedding methods to sample-based stochastic optimization and control. Specifically, we use the reduced-set expansion method as a way to discard sampled scenarios. The effect of such constraint removal is improved optimality and decreased conservativeness. This is achieved by solving a distributional-distance-regularized optimization problem. We demonstrated this optimization formulation is well-motivated in theory, computationally tractable, and effective in numerical algorithms.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-zhu20a, title = {A Kernel Mean Embedding Approach to Reducing Conservativeness in Stochastic Programming and Control}, author = {Zhu, Jia-Jie and Schoelkopf, Bernhard and Diehl, Moritz}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {915--923}, 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/zhu20a/zhu20a.pdf}, url = {https://proceedings.mlr.press/v120/zhu20a.html}, abstract = {In this paper, we apply kernel mean embedding methods to sample-based stochastic optimization and control. Specifically, we use the reduced-set expansion method as a way to discard sampled scenarios. The effect of such constraint removal is improved optimality and decreased conservativeness. This is achieved by solving a distributional-distance-regularized optimization problem. We demonstrated this optimization formulation is well-motivated in theory, computationally tractable, and effective in numerical algorithms. } }
Endnote
%0 Conference Paper %T A Kernel Mean Embedding Approach to Reducing Conservativeness in Stochastic Programming and Control %A Jia-Jie Zhu %A Bernhard Schoelkopf %A Moritz Diehl %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-zhu20a %I PMLR %P 915--923 %U https://proceedings.mlr.press/v120/zhu20a.html %V 120 %X In this paper, we apply kernel mean embedding methods to sample-based stochastic optimization and control. Specifically, we use the reduced-set expansion method as a way to discard sampled scenarios. The effect of such constraint removal is improved optimality and decreased conservativeness. This is achieved by solving a distributional-distance-regularized optimization problem. We demonstrated this optimization formulation is well-motivated in theory, computationally tractable, and effective in numerical algorithms.
APA
Zhu, J., Schoelkopf, B. & Diehl, M.. (2020). A Kernel Mean Embedding Approach to Reducing Conservativeness in Stochastic Programming and Control. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:915-923 Available from https://proceedings.mlr.press/v120/zhu20a.html.

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