Improve Single-Point Zeroth-Order Optimization Using High-Pass and Low-Pass Filters

Xin Chen, Yujie Tang, Na Li
Proceedings of the 39th International Conference on Machine Learning, PMLR 162:3603-3620, 2022.

Abstract

Single-point zeroth-order optimization (SZO) is useful in solving online black-box optimization and control problems in time-varying environments, as it queries the function value only once at each time step. However, the vanilla SZO method is known to suffer from a large estimation variance and slow convergence, which seriously limits its practical application. In this work, we borrow the idea of high-pass and low-pass filters from extremum seeking control (continuous-time version of SZO) and develop a novel SZO method called HLF-SZO by integrating these filters. It turns out that the high-pass filter coincides with the residual feedback method, and the low-pass filter can be interpreted as the momentum method. As a result, the proposed HLF-SZO achieves a much smaller variance and much faster convergence than the vanilla SZO method, and empirically outperforms the residual-feedback SZO method, which are verified via extensive numerical experiments.

Cite this Paper

BibTeX
@InProceedings{pmlr-v162-chen22w, title = {Improve Single-Point Zeroth-Order Optimization Using High-Pass and Low-Pass Filters}, author = {Chen, Xin and Tang, Yujie and Li, Na}, booktitle = {Proceedings of the 39th International Conference on Machine Learning}, pages = {3603--3620}, year = {2022}, editor = {Chaudhuri, Kamalika and Jegelka, Stefanie and Song, Le and Szepesvari, Csaba and Niu, Gang and Sabato, Sivan}, volume = {162}, series = {Proceedings of Machine Learning Research}, month = {17--23 Jul}, publisher = {PMLR}, pdf = {https://proceedings.mlr.press/v162/chen22w/chen22w.pdf}, url = {https://proceedings.mlr.press/v162/chen22w.html}, abstract = {Single-point zeroth-order optimization (SZO) is useful in solving online black-box optimization and control problems in time-varying environments, as it queries the function value only once at each time step. However, the vanilla SZO method is known to suffer from a large estimation variance and slow convergence, which seriously limits its practical application. In this work, we borrow the idea of high-pass and low-pass filters from extremum seeking control (continuous-time version of SZO) and develop a novel SZO method called HLF-SZO by integrating these filters. It turns out that the high-pass filter coincides with the residual feedback method, and the low-pass filter can be interpreted as the momentum method. As a result, the proposed HLF-SZO achieves a much smaller variance and much faster convergence than the vanilla SZO method, and empirically outperforms the residual-feedback SZO method, which are verified via extensive numerical experiments.} }
Endnote
%0 Conference Paper %T Improve Single-Point Zeroth-Order Optimization Using High-Pass and Low-Pass Filters %A Xin Chen %A Yujie Tang %A Na Li %B Proceedings of the 39th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2022 %E Kamalika Chaudhuri %E Stefanie Jegelka %E Le Song %E Csaba Szepesvari %E Gang Niu %E Sivan Sabato %F pmlr-v162-chen22w %I PMLR %P 3603--3620 %U https://proceedings.mlr.press/v162/chen22w.html %V 162 %X Single-point zeroth-order optimization (SZO) is useful in solving online black-box optimization and control problems in time-varying environments, as it queries the function value only once at each time step. However, the vanilla SZO method is known to suffer from a large estimation variance and slow convergence, which seriously limits its practical application. In this work, we borrow the idea of high-pass and low-pass filters from extremum seeking control (continuous-time version of SZO) and develop a novel SZO method called HLF-SZO by integrating these filters. It turns out that the high-pass filter coincides with the residual feedback method, and the low-pass filter can be interpreted as the momentum method. As a result, the proposed HLF-SZO achieves a much smaller variance and much faster convergence than the vanilla SZO method, and empirically outperforms the residual-feedback SZO method, which are verified via extensive numerical experiments.
APA
Chen, X., Tang, Y. & Li, N.. (2022). Improve Single-Point Zeroth-Order Optimization Using High-Pass and Low-Pass Filters. Proceedings of the 39th International Conference on Machine Learning, in Proceedings of Machine Learning Research 162:3603-3620 Available from https://proceedings.mlr.press/v162/chen22w.html.

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