Sliding-Seeking Control: Model-Free Optimization with Safety Constraints

Felipe Galarza-Jiménez, Jorge Poveda, Emiliano Dall’Anese
Proceedings of The 4th Annual Learning for Dynamics and Control Conference, PMLR 168:1100-1111, 2022.

Abstract

This paper considers the design of online model-free algorithms for the solution of convex optimization problems with a time-varying cost function. We propose an online switched zeroth-order algorithm where: i) different vector fields are implemented based on whether constraints are satisfied; and, ii) zeroth-order dynamics are leveraged to obtain estimates of the (time-varying) gradients in the algorithmic updates. The zeroth-order strategy is suitable for cases where the optimizer has access to functional evaluations of the cost and constraints, but has no knowledge of their functional form. The proposed online algorithm guarantees finite-time feasibility (while avoiding projections) and it exhibits asymptotic stability to a neighborhood of the optimal trajectory of the time-varying problem. Results are established for cost functions that are strictly convex and twice continuously differentiable. Illustrative numerical results are presented to showcase the main properties of the algorithm.

Cite this Paper

BibTeX
@InProceedings{pmlr-v168-galarza-jimenez22a, title = {Sliding-Seeking Control: Model-Free Optimization with Safety Constraints}, author = {Galarza-Jim\'enez, Felipe and Poveda, Jorge and Dall'Anese, Emiliano}, booktitle = {Proceedings of The 4th Annual Learning for Dynamics and Control Conference}, pages = {1100--1111}, year = {2022}, editor = {Firoozi, Roya and Mehr, Negar and Yel, Esen and Antonova, Rika and Bohg, Jeannette and Schwager, Mac and Kochenderfer, Mykel}, volume = {168}, series = {Proceedings of Machine Learning Research}, month = {23--24 Jun}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v168/galarza-jimenez22a/galarza-jimenez22a.pdf}, url = {https://proceedings.mlr.press/v168/galarza-jimenez22a.html}, abstract = {This paper considers the design of online model-free algorithms for the solution of convex optimization problems with a time-varying cost function. We propose an online switched zeroth-order algorithm where: i) different vector fields are implemented based on whether constraints are satisfied; and, ii) zeroth-order dynamics are leveraged to obtain estimates of the (time-varying) gradients in the algorithmic updates. The zeroth-order strategy is suitable for cases where the optimizer has access to functional evaluations of the cost and constraints, but has no knowledge of their functional form. The proposed online algorithm guarantees finite-time feasibility (while avoiding projections) and it exhibits asymptotic stability to a neighborhood of the optimal trajectory of the time-varying problem. Results are established for cost functions that are strictly convex and twice continuously differentiable. Illustrative numerical results are presented to showcase the main properties of the algorithm.} }
Endnote
%0 Conference Paper %T Sliding-Seeking Control: Model-Free Optimization with Safety Constraints %A Felipe Galarza-Jiménez %A Jorge Poveda %A Emiliano Dall’Anese %B Proceedings of The 4th Annual Learning for Dynamics and Control Conference %C Proceedings of Machine Learning Research %D 2022 %E Roya Firoozi %E Negar Mehr %E Esen Yel %E Rika Antonova %E Jeannette Bohg %E Mac Schwager %E Mykel Kochenderfer %F pmlr-v168-galarza-jimenez22a %I PMLR %P 1100--1111 %U https://proceedings.mlr.press/v168/galarza-jimenez22a.html %V 168 %X This paper considers the design of online model-free algorithms for the solution of convex optimization problems with a time-varying cost function. We propose an online switched zeroth-order algorithm where: i) different vector fields are implemented based on whether constraints are satisfied; and, ii) zeroth-order dynamics are leveraged to obtain estimates of the (time-varying) gradients in the algorithmic updates. The zeroth-order strategy is suitable for cases where the optimizer has access to functional evaluations of the cost and constraints, but has no knowledge of their functional form. The proposed online algorithm guarantees finite-time feasibility (while avoiding projections) and it exhibits asymptotic stability to a neighborhood of the optimal trajectory of the time-varying problem. Results are established for cost functions that are strictly convex and twice continuously differentiable. Illustrative numerical results are presented to showcase the main properties of the algorithm.
APA
Galarza-Jiménez, F., Poveda, J. & Dall’Anese, E.. (2022). Sliding-Seeking Control: Model-Free Optimization with Safety Constraints. Proceedings of The 4th Annual Learning for Dynamics and Control Conference, in Proceedings of Machine Learning Research 168:1100-1111 Available from https://proceedings.mlr.press/v168/galarza-jimenez22a.html.

Related Material