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	<title>Learning-Based Abstractions for Nonlinear Constraint Solving - Revision history</title>
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	<updated>2026-04-16T03:20:40Z</updated>
	<subtitle>Revision history for this page on the wiki</subtitle>
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		<id>https://murray.cds.caltech.edu/index.php?title=Learning-Based_Abstractions_for_Nonlinear_Constraint_Solving&amp;diff=21463&amp;oldid=prev</id>
		<title>Murray at 17:09, 23 July 2017</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Learning-Based_Abstractions_for_Nonlinear_Constraint_Solving&amp;diff=21463&amp;oldid=prev"/>
		<updated>2017-07-23T17:09:48Z</updated>

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				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;← Older revision&lt;/td&gt;
				&lt;td colspan=&quot;2&quot; style=&quot;background-color: #fff; color: #202122; text-align: center;&quot;&gt;Revision as of 17:09, 23 July 2017&lt;/td&gt;
				&lt;/tr&gt;&lt;tr&gt;&lt;td colspan=&quot;2&quot; class=&quot;diff-lineno&quot; id=&quot;mw-diff-left-l6&quot;&gt;Line 6:&lt;/td&gt;
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&lt;tr&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|URL=http://www.cds.caltech.edu/~murray/preprints/dagm17-ijcai.pdf&lt;/div&gt;&lt;/td&gt;&lt;td class=&quot;diff-marker&quot;&gt;&lt;/td&gt;&lt;td style=&quot;background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;&quot;&gt;&lt;div&gt;|URL=http://www.cds.caltech.edu/~murray/preprints/dagm17-ijcai.pdf&lt;/div&gt;&lt;/td&gt;&lt;/tr&gt;
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		<author><name>Murray</name></author>
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	<entry>
		<id>https://murray.cds.caltech.edu/index.php?title=Learning-Based_Abstractions_for_Nonlinear_Constraint_Solving&amp;diff=21462&amp;oldid=prev</id>
		<title>Murray: Created page with &quot;{{Paper |Title=Learning-Based Abstractions for Nonlinear Constraint Solving |Authors=Sumanth Dathathri, Nikos Arechiga, Sicun Gao, and Richard M. Murray |Source=2017 Internati...&quot;</title>
		<link rel="alternate" type="text/html" href="https://murray.cds.caltech.edu/index.php?title=Learning-Based_Abstractions_for_Nonlinear_Constraint_Solving&amp;diff=21462&amp;oldid=prev"/>
		<updated>2017-07-23T17:09:39Z</updated>

		<summary type="html">&lt;p&gt;Created page with &amp;quot;{{Paper |Title=Learning-Based Abstractions for Nonlinear Constraint Solving |Authors=Sumanth Dathathri, Nikos Arechiga, Sicun Gao, and Richard M. Murray |Source=2017 Internati...&amp;quot;&lt;/p&gt;
&lt;p&gt;&lt;b&gt;New page&lt;/b&gt;&lt;/p&gt;&lt;div&gt;{{Paper&lt;br /&gt;
|Title=Learning-Based Abstractions for Nonlinear Constraint Solving&lt;br /&gt;
|Authors=Sumanth Dathathri, Nikos Arechiga, Sicun Gao, and Richard M. Murray&lt;br /&gt;
|Source=2017 International Joint Conference on Artificial Intelligence (IJCAI)&lt;br /&gt;
|Abstract=We propose a new abstraction refinement procedure based on machine learning to improve the performance of nonlinear constraint solving algorithms on large-scale problems. The proposed approach decomposes the original set of constraints into smaller subsets, and uses learning algorithms to propose sequences of abstractions that take the form of conjunctions of classifiers. The core procedure is a refinement loop that keeps improving the learned results based on counterexamples that are obtained from partial constraints that are easy to solve. Experiments show that the proposed techniques significantly improve the performance of state-of-the-art constraint solvers on many challenging benchmarks. The mechanism is capable of producing intermediate symbolic abstractions that are also important for many applications and for understanding the internal structures of hard constraint solving problems.&lt;br /&gt;
|URL=http://www.cds.caltech.edu/~murray/preprints/dagm17-ijcai.pdf&lt;br /&gt;
|Type=Conference paper&lt;br /&gt;
|ID=2017e&lt;br /&gt;
|Tag=dagm17-ijca&lt;br /&gt;
|Funding=SRC TerraSwarm&lt;br /&gt;
}}&lt;/div&gt;</summary>
		<author><name>Murray</name></author>
	</entry>
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