A Dynamical Systems Perspective on Nesterov Acceleration

@InProceedings{pmlr-v97-muehlebach19a,
  title = 	 {A Dynamical Systems Perspective on {N}esterov Acceleration},
  author =       {Muehlebach, Michael and Jordan, Michael},
  booktitle = 	 {Proceedings of the 36th International Conference on Machine Learning},
  pages = 	 {4656--4662},
  year = 	 {2019},
  editor = 	 {Chaudhuri, Kamalika and Salakhutdinov, Ruslan},
  volume = 	 {97},
  series = 	 {Proceedings of Machine Learning Research},
  month = 	 {09--15 Jun},
  publisher =    {PMLR},
  pdf = 	 {http://proceedings.mlr.press/v97/muehlebach19a/muehlebach19a.pdf},
  url = 	 {https://proceedings.mlr.press/v97/muehlebach19a.html},
  abstract = 	 {We present a dynamical system framework for understanding Nesterov’s accelerated gradient method. In contrast to earlier work, our derivation does not rely on a vanishing step size argument. We show that Nesterov acceleration arises from discretizing an ordinary differential equation with a semi-implicit Euler integration scheme. We analyze both the underlying differential equation as well as the discretization to obtain insights into the phenomenon of acceleration. The analysis suggests that a curvature-dependent damping term lies at the heart of the phenomenon. We further establish connections between the discretized and the continuous-time dynamics.}
}