CaltechAUTHORS
  A Caltech Library Service

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

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 (Unpublished) https://resolver.caltech.edu/CaltechAUTHORS:20190401-123307245

[img] PDF - Submitted Version
See Usage Policy.

497Kb

Use this Persistent URL to link to this item: https://resolver.caltech.edu/CaltechAUTHORS:20190401-123307245

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)
Related URLs:
URLURL TypeDescription
http://arxiv.org/abs/1602.05908arXivDiscussion Paper
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

Repository Staff Only: item control page