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 feasible 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
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
2004
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
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, .
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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 feasible 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
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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
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Date deposited: 03 Aug 2004
Last modified: 14 Mar 2024 06:27
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Contributors
Author:
Thore Graepel
Author:
Ralf Herbrich
Author:
Andriy Kharechko
Author:
John Shawe-Taylor
Editor:
Sebastian Thrun
Editor:
Lawrence Saul
Editor:
Bernhard Scholkopf
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