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
Chicago
ICMJE
MLA
NLM
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