Learning the Globally Optimal Distributed LQ Regulator

Luca Furieri, Yang Zheng, Maryam Kamgarpour
Proceedings of the 2nd Conference on Learning for Dynamics and Control, PMLR 120:287-297, 2020.

Abstract

We study model-free learning methods for the output-feedback Linear Quadratic (LQ) control problem in finite-horizon subject to subspace constraints on the control policy. Subspace constraints naturally arise in the field of distributed control and present a significant challenge in the sense that standard model-based optimization and learning leads to intractable numerical programs in general. Building upon recent results in zeroth-order optimization, we establish model-free sample-complexity bounds for the class of distributed LQ problems where a local gradient dominance constant exists on any sublevel set of the cost function. We prove that a fundamental class of distributed control problems - commonly referred to as Quadratically Invariant (QI) problems - as well as others possess this property. To the best of our knowledge, our result is the first sample-complexity bound guarantee on learning globally optimal distributed output-feedback control policies.

Cite this Paper

BibTeX
@InProceedings{pmlr-v120-furieri20a, title = {Learning the Globally Optimal Distributed LQ Regulator}, author = {Furieri, Luca and Zheng, Yang and Kamgarpour, Maryam}, booktitle = {Proceedings of the 2nd Conference on Learning for Dynamics and Control}, pages = {287--297}, 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/furieri20a/furieri20a.pdf}, url = {https://proceedings.mlr.press/v120/furieri20a.html}, abstract = {We study model-free learning methods for the output-feedback Linear Quadratic (LQ) control problem in finite-horizon subject to subspace constraints on the control policy. Subspace constraints naturally arise in the field of distributed control and present a significant challenge in the sense that standard model-based optimization and learning leads to intractable numerical programs in general. Building upon recent results in zeroth-order optimization, we establish model-free sample-complexity bounds for the class of distributed LQ problems where a local gradient dominance constant exists on any sublevel set of the cost function. We prove that a fundamental class of distributed control problems - commonly referred to as Quadratically Invariant (QI) problems - as well as others possess this property. To the best of our knowledge, our result is the first sample-complexity bound guarantee on learning globally optimal distributed output-feedback control policies. } }
Endnote
%0 Conference Paper %T Learning the Globally Optimal Distributed LQ Regulator %A Luca Furieri %A Yang Zheng %A Maryam Kamgarpour %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-furieri20a %I PMLR %P 287--297 %U https://proceedings.mlr.press/v120/furieri20a.html %V 120 %X We study model-free learning methods for the output-feedback Linear Quadratic (LQ) control problem in finite-horizon subject to subspace constraints on the control policy. Subspace constraints naturally arise in the field of distributed control and present a significant challenge in the sense that standard model-based optimization and learning leads to intractable numerical programs in general. Building upon recent results in zeroth-order optimization, we establish model-free sample-complexity bounds for the class of distributed LQ problems where a local gradient dominance constant exists on any sublevel set of the cost function. We prove that a fundamental class of distributed control problems - commonly referred to as Quadratically Invariant (QI) problems - as well as others possess this property. To the best of our knowledge, our result is the first sample-complexity bound guarantee on learning globally optimal distributed output-feedback control policies.
APA
Furieri, L., Zheng, Y. & Kamgarpour, M.. (2020). Learning the Globally Optimal Distributed LQ Regulator. Proceedings of the 2nd Conference on Learning for Dynamics and Control, in Proceedings of Machine Learning Research 120:287-297 Available from https://proceedings.mlr.press/v120/furieri20a.html.

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