Efficient approaches for escaping higher order saddle points in non-convex optimization
Conference Paper
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 Authors
Cited Authors
- Anandkumar, A; Ge, R
Published Date
- June 6, 2016
Published In
Volume / Issue
- 49 / June
Start / End Page
- 81 - 102
Electronic International Standard Serial Number (EISSN)
- 1533-7928
International Standard Serial Number (ISSN)
- 1532-4435
Citation Source
- Scopus