Faster convex optimization: Simulated annealing with an efficient universal barrier

Jacob Abernethy, Elad Hazan

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

1 Scopus citations

Abstract

This paper explores a surprising equivalence between two seemingly-distinct convex optimization methods. We show that simulated annealing, a well-studied random walk algorithms, is directly equivalent, in a certain sense, to the central path interior point algorithm for the the en- tropic universal barrier function. This connection exhibits several benefits. First, we are able improve the state of the art time complexity for convex optimization under the membership oracle model by devising a new temperature schedule for simulated annealing motivated by central path following interior point methods. Second, we get an efficient randomized interior point method with an efficiently computable universal barrier for any convex set described by a membership oracle. Previously, efficiently computable barriers were known only for particular convex sets.

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)
Pages3734-3746
Number of pages13
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
Volume6

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

Fingerprint Dive into the research topics of 'Faster convex optimization: Simulated annealing with an efficient universal barrier'. Together they form a unique fingerprint.

  • Cite this

    Abernethy, J., & Hazan, E. (2016). Faster convex optimization: Simulated annealing with an efficient universal barrier. In K. Q. Weinberger, & M. F. Balcan (Eds.), 33rd International Conference on Machine Learning, ICML 2016 (pp. 3734-3746). (33rd International Conference on Machine Learning, ICML 2016; Vol. 6). International Machine Learning Society (IMLS).