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Xiaoxia (Shirley) Wu, 12th floor lounge: Acceleration via Symplectic Discretization of High-Resolution Differential Equations
Friday, March 01, 2019, 01:00pm - 02:00pm
We study first-order optimization methods obtained by discretizingordinary differential equations (ODEs) corresponding to Nesterov'saccelerated gradient methods (NAGs) and Polyak's heavy-ball method.We consider three discretization schemes: an explicit Euler scheme,an implicit Euler scheme, and a symplectic scheme. We show thatthe optimization algorithm generated by applying the symplecticscheme to a high-resolution ODE proposed by Shi et al. [2018]achieves an accelerated rate for minimizing smooth strongly convexfunctions. On the other hand, the resulting algorithm eitherfails to achieve acceleration or is impractical when the schemeis implicit, the ODE is low-resolution, or the scheme is explicit.This is a background talk for next week's colloquium given byAngelia Nedich.
Location: 12th floor lounge

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