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

Wed Jun 12 06:30 PM -- 09:00 PM (PDT) @ Pacific Ballroom #205

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.

Author Information

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

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