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First-order methods almost always avoid strict saddle points

Lee, Jason D. ; Panageas, Ioannis ; Piliouras, Georgios ; Simchowitz, Max ; Jordan, Michael I. ; Recht, Benjamin

Mathematical programming, 2019-07, Vol.176 (1-2), p.311-337 [Periódico revisado por pares]

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Título:
First-order methods almost always avoid strict saddle points
Autor: Lee, Jason D. ; Panageas, Ioannis ; Piliouras, Georgios ; Simchowitz, Max ; Jordan, Michael I. ; Recht, Benjamin
Assuntos: Algorithms ; Calculus of Variations and Optimal Control; Optimization ; Combinatorics ; Full Length Paper ; Manifolds ; Mathematical and Computational Physics ; Mathematical Methods in Physics ; Mathematical programming ; Mathematics ; Mathematics and Statistics ; Mathematics of Computing ; Numerical Analysis ; Saddle points ; Stability analysis ; Theoretical
É parte de: Mathematical programming, 2019-07, Vol.176 (1-2), p.311-337
Descrição: We establish that first-order methods avoid strict saddle points for almost all initializations. Our results apply to a wide variety of first-order methods, including (manifold) gradient descent, block coordinate descent, mirror descent and variants thereof. The connecting thread is that such algorithms can be studied from a dynamical systems perspective in which appropriate instantiations of the Stable Manifold Theorem allow for a global stability analysis. Thus, neither access to second-order derivative information nor randomness beyond initialization is necessary to provably avoid strict saddle points.
Editor: Berlin/Heidelberg: Springer Berlin Heidelberg
Idioma: Inglês

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