Anandkumar, Anima and Ge, Rong (2016) Efficient approaches for escaping higher order saddle points in non-convex optimization. . (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20190401-123307245
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Abstract
Local search heuristics for non-convex optimizations are popular in applied machine learning. However, in general it is hard to guarantee that such algorithms even converge to a local minimum, due to the existence of complicated saddle point structures in high dimensions. Many functions have degenerate saddle points such that the first and second order derivatives cannot distinguish them with local optima. In this paper we use higher order derivatives to escape these saddle points: we design the first efficient algorithm guaranteed to converge to a third order local optimum (while existing techniques are at most second order). We also show that it is NP-hard to extend this further to finding fourth order local optima.
Item Type: | Report or Paper (Discussion Paper) | ||||||
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Record Number: | CaltechAUTHORS:20190401-123307245 | ||||||
Persistent URL: | https://resolver.caltech.edu/CaltechAUTHORS:20190401-123307245 | ||||||
Usage Policy: | No commercial reproduction, distribution, display or performance rights in this work are provided. | ||||||
ID Code: | 94323 | ||||||
Collection: | CaltechAUTHORS | ||||||
Deposited By: | George Porter | ||||||
Deposited On: | 01 Apr 2019 22:41 | ||||||
Last Modified: | 03 Oct 2019 21:02 |
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