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