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Gradient Descent only Converges to Minimizers

Jason D. Lee(jasondlee88***at***gmail.com)
Max Simchowitz(msimchowitz***at***berkeley.edu)
Michael I. Jordan(jordan***at***cs.berkeley.edu)
Benjamin Recht(brecht***at***berkeley.edu)

Abstract: We show that gradient descent converges to a local minimizer, almost surely with random initialization. This is proved by applying the Stable Manifold Theorem from dynamical systems theory.

Keywords: Gradient descent, non-convex, saddle points, local minimizer,

Category 1: Nonlinear Optimization (Unconstrained Optimization )


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Entry Submitted: 02/17/2016
Entry Accepted: 02/17/2016
Entry Last Modified: 02/17/2016

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