Ordinary differential equations, and in general a dynamical system viewpoint, have seen a resurgence of interest in developing fast optimization methods, mainly thanks to the availability of well-established analysis tools. In this study, we pursue a similar objective and propose a class of hybrid control systems that adopts a 2nd-order differential equation as its continuous flow. A distinctive feature of the proposed differential equation in comparison with the existing literature is a state-dependent, time-invariant damping term that acts as a feedback control input. Given a user-defined scalar α, it is shown that the proposed control input steers the state trajectories to the global optimizer of a desired objective function with a guaranteed rate of convergence O(e−αt). Our framework requires that the objective function satisfies the so called Polyak–{Ł}ojasiewicz inequality. Furthermore, a discretization method is introduced such that the resulting discrete dynamical system possesses an exponential rate of convergence.
Original languageEnglish
Title of host publicationProceedings of the 35th International Conference on Machine Learning (ICML 2018)
EditorsJennifer Dy, Andreas Krause
PublisherMLR Press
Publication statusPublished - 2018
EventICML 2018: 35th International Conference on Machine Learning - Stockholm, Sweden
Duration: 10 Jul 201815 Jul 2018

Publication series

NameProceedings of Machine Learning Research (PMLR)
ISSN (Electronic)1938-7228


ConferenceICML 2018: 35th International Conference on Machine Learning

ID: 46700357