A Generic Approach for Escaping Saddle points

Abstract : A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points. First-order methods often get stuck at saddle points, greatly deteriorating their performance. Typically, to escape from saddles one has to use second-order methods. However, most works on second-order methods rely extensively on expensive Hessian-based computations, making them impractical in large-scale settings. To tackle this challenge, we introduce a generic framework that minimizes Hessian based computations while at the same time provably converging to second-order critical points. Our framework carefully alternates between a first-order and a second-order subroutine, using the latter only close to saddle points, and yields convergence results competitive to the state-of-the-art. Empirical results suggest that our strategy also enjoys a good practical performance.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01652150
Contributeur : Francis Bach <>
Soumis le : jeudi 30 novembre 2017 - 07:56:23
Dernière modification le : jeudi 26 avril 2018 - 10:28:58

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  • HAL Id : hal-01652150, version 1
  • ARXIV : 1709.01434

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Sashank J Reddi, Manzil Zaheer, Suvrit Sra, Barnabas Poczos, Francis Bach, et al.. A Generic Approach for Escaping Saddle points. 2017. 〈hal-01652150〉

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