A Differential Equation for Modeling Nesterov’s Accelerated Gradient Method: Theory and Insights

Part of Advances in Neural Information Processing Systems 27 (NIPS 2014)

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Authors

Weijie Su, Stephen Boyd, Emmanuel Candes

Abstract

<p>We derive a second-order ordinary differential equation (ODE), which is the limit of Nesterov’s accelerated gradient method. This ODE exhibits approximate equivalence to Nesterov’s scheme and thus can serve as a tool for analysis. We show that the continuous time ODE allows for a better understanding of Nesterov’s scheme. As a byproduct, we obtain a family of schemes with similar convergence rates. The ODE interpretation also suggests restarting Nesterov’s scheme leading to an algorithm, which can be rigorously proven to converge at a linear rate whenever the objective is strongly convex.</p>