On graduated optimization for stochastic non-convex problems

Elad Hazan, Kfir Y. Levy, Shai Shalev-Shwartz

Research output: Chapter in Book/Report/Conference proceedingConference contribution

7 Scopus citations

Abstract

The graduated optimization approach, also known as the continuation method, is a popular heuristic to solving non-convcx problems that has received renewed interest over the last decade. Despite being popular, very little is known in terms of its theoretical convergence analysis. In this paper we describe a new first-order algorithm based on graduated optimization and analyze its performance. We characterize a family of non-convex functions for which this algorithm provably converges to a global optimum. In particular, we prove that the algorithm converges to an ϵ-approximate solution within O( 1/ϵ4) gradient-based steps. We extend our algorithm and analysis to the setting of stochastic non-convex optimization with noisy gradient feedback, attaining the same convergence rate. Additionally, we discuss the setting of "zero- order optimization", and devise a variant of our algorithm which converges at rate of O(d24).

Original languageEnglish (US)
Title of host publication33rd International Conference on Machine Learning, ICML 2016
EditorsKilian Q. Weinberger, Maria Florina Balcan
PublisherInternational Machine Learning Society (IMLS)
Pages2726-2739
Number of pages14
ISBN (Electronic)9781510829008
StatePublished - Jan 1 2016
Event33rd International Conference on Machine Learning, ICML 2016 - New York City, United States
Duration: Jun 19 2016Jun 24 2016

Publication series

Name33rd International Conference on Machine Learning, ICML 2016
Volume4

Other

Other33rd International Conference on Machine Learning, ICML 2016
CountryUnited States
CityNew York City
Period6/19/166/24/16

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence
  • Software
  • Computer Networks and Communications

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  • Cite this

    Hazan, E., Levy, K. Y., & Shalev-Shwartz, S. (2016). On graduated optimization for stochastic non-convex problems. In K. Q. Weinberger, & M. F. Balcan (Eds.), 33rd International Conference on Machine Learning, ICML 2016 (pp. 2726-2739). (33rd International Conference on Machine Learning, ICML 2016; Vol. 4). International Machine Learning Society (IMLS).