TR2020-100
Finite-Time Convergence in Continuous-Time Optimization
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- "Finite-Time Convergence in Continuous-Time Optimization", International Conference on Machine Learning (ICML), July 2020.BibTeX TR2020-100 PDF
- @inproceedings{Romero2020jul,
- author = {Romero, Orlando and Benosman, Mouhacine},
- title = {Finite-Time Convergence in Continuous-Time Optimization},
- booktitle = {International Conference on Machine Learning},
- year = 2020,
- month = jul,
- url = {https://www.merl.com/publications/TR2020-100}
- }
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- "Finite-Time Convergence in Continuous-Time Optimization", International Conference on Machine Learning (ICML), July 2020.
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MERL Contact:
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Research Area:
Abstract:
In this paper, we investigate a Lyapunov-like differential inequality that allows us to establish finite-time stability of a continuous-time state-space dynamical system represented via a multivariate ordinary differential equation or differential inclusion. Equipped with this condition, we synthesize first and second-order (in an optimization variable) dynamical systems that achieve finite-time convergence to the minima of a given sufficiently regular cost function. As a byproduct, we show that the q-rescaled gradient flow (q-RGF) proposed by Wibisono et al. (2016) is indeed finite-time convergent, provided the cost function is gradient dominated of order p E (1, q). This way, we effectively bridge a gap between the q-RGF and the finite-time convergent normalized gradient flow (NGF) (q = infinity) proposed by Cortes' (2006) in his seminal paper in the context of multiagent systems. We discuss strategies to discretize our proposed flows and conclude by conducting some numerical experiments to illustrate our results.
Related News & Events
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NEWS MERL researchers presenting three papers at ICML 2020 Date: July 12, 2020 - July 18, 2020
Where: Vienna, Austria (virtual this year)
MERL Contacts: Mouhacine Benosman; Anoop Cherian; Devesh K. Jha; Daniel N. Nikovski
Research Areas: Artificial Intelligence, Computer Vision, Data Analytics, Dynamical Systems, Machine Learning, Optimization, RoboticsBrief- MERL researchers are presenting three papers at the International Conference on Machine Learning (ICML 2020), which is virtually held this year from 12-18th July. ICML is one of the top-tier conferences in machine learning with an acceptance rate of 22%. The MERL papers are:
1) "Finite-time convergence in Continuous-Time Optimization" by Orlando Romero and Mouhacine Benosman.
2) "Can Increasing Input Dimensionality Improve Deep Reinforcement Learning?" by Kei Ota, Tomoaki Oiki, Devesh Jha, Toshisada Mariyama, and Daniel Nikovski.
3) "Representation Learning Using Adversarially-Contrastive Optimal Transport" by Anoop Cherian and Shuchin Aeron.
- MERL researchers are presenting three papers at the International Conference on Machine Learning (ICML 2020), which is virtually held this year from 12-18th July. ICML is one of the top-tier conferences in machine learning with an acceptance rate of 22%. The MERL papers are: