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Efficient approaches for escaping higher order saddle points in non-convex optimization

Publication ,  Conference
Anandkumar, A; Ge, R
Published in: Journal of Machine Learning Research
June 6, 2016

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.

Duke Scholars

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

June 6, 2016

Volume

49

Issue

June

Start / End Page

81 / 102

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences
 

Citation

APA
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ICMJE
MLA
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Anandkumar, A., & Ge, R. (2016). Efficient approaches for escaping higher order saddle points in non-convex optimization. In Journal of Machine Learning Research (Vol. 49, pp. 81–102).
Anandkumar, A., and R. Ge. “Efficient approaches for escaping higher order saddle points in non-convex optimization.” In Journal of Machine Learning Research, 49:81–102, 2016.
Anandkumar A, Ge R. Efficient approaches for escaping higher order saddle points in non-convex optimization. In: Journal of Machine Learning Research. 2016. p. 81–102.
Anandkumar, A., and R. Ge. “Efficient approaches for escaping higher order saddle points in non-convex optimization.” Journal of Machine Learning Research, vol. 49, no. June, 2016, pp. 81–102.
Anandkumar A, Ge R. Efficient approaches for escaping higher order saddle points in non-convex optimization. Journal of Machine Learning Research. 2016. p. 81–102.

Published In

Journal of Machine Learning Research

EISSN

1533-7928

ISSN

1532-4435

Publication Date

June 6, 2016

Volume

49

Issue

June

Start / End Page

81 / 102

Related Subject Headings

  • Artificial Intelligence & Image Processing
  • 4905 Statistics
  • 4611 Machine learning
  • 17 Psychology and Cognitive Sciences
  • 08 Information and Computing Sciences