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Revisiting the Role of Euler Numerical Integration on Acceleration and Stability in Convex Optimization (2102.11537v1)

Published 23 Feb 2021 in math.OC and cs.LG

Abstract: Viewing optimization methods as numerical integrators for ordinary differential equations (ODEs) provides a thought-provoking modern framework for studying accelerated first-order optimizers. In this literature, acceleration is often supposed to be linked to the quality of the integrator (accuracy, energy preservation, symplecticity). In this work, we propose a novel ordinary differential equation that questions this connection: both the explicit and the semi-implicit (a.k.a symplectic) Euler discretizations on this ODE lead to an accelerated algorithm for convex programming. Although semi-implicit methods are well-known in numerical analysis to enjoy many desirable features for the integration of physical systems, our findings show that these properties do not necessarily relate to acceleration.

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Authors (5)
  1. Peiyuan Zhang (24 papers)
  2. Antonio Orvieto (46 papers)
  3. Hadi Daneshmand (20 papers)
  4. Thomas Hofmann (121 papers)
  5. Roy Smith (1 paper)
Citations (7)

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