A Dynamical Systems Perspective on Nesterov Acceleration


Michael Muehlebach, Michael Jordan ;
Proceedings of the 36th International Conference on Machine Learning, PMLR 97:4656-4662, 2019.


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.

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