The University of Southampton
University of Southampton Institutional Repository

Semidefinite Programming by Perceptron Learning

Semidefinite Programming by Perceptron Learning
Semidefinite Programming by Perceptron Learning
We present a modified version of the perceptron learning algorithm (PLA) which solves semidefinite programs (SDPs) in polynomial time. The algorithm is based on the following three observations: (i) Semidefinite programs are linear programs with infinitely many (linear) constraints; (ii) every linear program can be solved by a sequence of constraint satisfaction problems with linear constraints; (iii) in general, the perceptron learning algorithm solves a constraint satisfaction problem with linear constraints in finitely many updates. Combining the PLA with a probabilistic rescaling algorithm (which, on average, increases the size of the feasable region) results in a probabilistic algorithm for solving SDPs that runs in polynomial time. We present preliminary results which demonstrate that the algorithm works, but is not competitive with state-of-the-art interior point methods.
Semidefinite programming, perceptron learning, optimization, probabilistic algorithm, MAXCUT.
0262201526
457-465
MIT Press
Graepel, Thore
f01fa538-c0f8-4e36-bbcc-698366e73f39
Herbrich, Ralf
3024ba7e-f3a1-4187-8655-b7f163c7c733
Kharechko, Andriy
9dccd719-b3fd-4ff6-9b85-b329e31cba9e
Shawe-Taylor, John
b1931d97-fdd0-4bc1-89bc-ec01648e928b
Thrun, Sebastian
Saul, Lawrence
Scholkopf, Bernhard
Graepel, Thore
f01fa538-c0f8-4e36-bbcc-698366e73f39
Herbrich, Ralf
3024ba7e-f3a1-4187-8655-b7f163c7c733
Kharechko, Andriy
9dccd719-b3fd-4ff6-9b85-b329e31cba9e
Shawe-Taylor, John
b1931d97-fdd0-4bc1-89bc-ec01648e928b
Thrun, Sebastian
Saul, Lawrence
Scholkopf, Bernhard

Graepel, Thore, Herbrich, Ralf, Kharechko, Andriy and Shawe-Taylor, John (2004) Semidefinite Programming by Perceptron Learning. In, Thrun, Sebastian, Saul, Lawrence and Scholkopf, Bernhard (eds.) Advances in Neural Information Processing Systems 16. MIT Press, pp. 457-465.

Record type: Book Section

Abstract

We present a modified version of the perceptron learning algorithm (PLA) which solves semidefinite programs (SDPs) in polynomial time. The algorithm is based on the following three observations: (i) Semidefinite programs are linear programs with infinitely many (linear) constraints; (ii) every linear program can be solved by a sequence of constraint satisfaction problems with linear constraints; (iii) in general, the perceptron learning algorithm solves a constraint satisfaction problem with linear constraints in finitely many updates. Combining the PLA with a probabilistic rescaling algorithm (which, on average, increases the size of the feasable region) results in a probabilistic algorithm for solving SDPs that runs in polynomial time. We present preliminary results which demonstrate that the algorithm works, but is not competitive with state-of-the-art interior point methods.

Text
NIPS2003_AA58.pdf - Other
Download (268kB)

More information

Published date: 2004
Additional Information: Chapter: 8 Address: Cambridge, MA
Keywords: Semidefinite programming, perceptron learning, optimization, probabilistic algorithm, MAXCUT.
Organisations: Electronics & Computer Science

Identifiers

Local EPrints ID: 259597
URI: http://eprints.soton.ac.uk/id/eprint/259597
ISBN: 0262201526
PURE UUID: 07f3fdef-6ac4-40e2-87a7-4a2df2a01307

Catalogue record

Date deposited: 03 Aug 2004
Last modified: 09 Dec 2019 20:15

Export record

Contributors

Author: Thore Graepel
Author: Ralf Herbrich
Author: Andriy Kharechko
Author: John Shawe-Taylor
Editor: Sebastian Thrun
Editor: Lawrence Saul
Editor: Bernhard Scholkopf

University divisions

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×