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A Dynamical Systems Perspective on Nesterov Acceleration
Michael Muehlebach · Michael Jordan

Wed Jun 12 04:35 PM -- 04:40 PM (PDT) @ Room 103
in Convex Optimization »

This article presents a dynamic system model describing Nesterov's accelerated gradient method. In contrast to earlier work, the derivation does not rely on a vanishing step size argument. It is shown that Nesterov's accelerated gradient method follows from discretizing an ordinary differential equation with a semi-implicit Euler integration scheme. We analyze both the corresponding differential equation as well as the discretization for obtaining insights into the phenomenon of acceleration. The analysis suggests that a curvature-dependent damping term lies at the heart of acceleration. We further establish connections between the discretized and the continuous-time dynamics.

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Author Information

Michael Muehlebach (UC Berkeley)
Michael Jordan (UC Berkeley)

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