The complexity of unsupervised learning of lexicographic preferences
13th Multidisciplinary Workshop on Advances in Preference Handling, Jul 2022, Vienne, Austria This paper considers the task of learning users' preferences on a combinatorial set of alternatives, as generally used by online configurators, for example. In many settings, only a set of selected alt...
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| creator | Fargier, Hélène Gimenez, Pierre-François Mengin, Jérôme Nguyen, Bao Ngoc Le |
| description | 13th Multidisciplinary Workshop on Advances in Preference
Handling, Jul 2022, Vienne, Austria This paper considers the task of learning users' preferences on a
combinatorial set of alternatives, as generally used by online configurators,
for example. In many settings, only a set of selected alternatives during past
interactions is available to the learner. Fargier et al. [2018] propose an
approach to learn, in such a setting, a model of the users' preferences that
ranks previously chosen alternatives as high as possible; and an algorithm to
learn, in this setting, a particular model of preferences: lexicographic
preferences trees (LP-trees). In this paper, we study complexity-theoretical
problems related to this approach. We give an upper bound on the sample
complexity of learning an LP-tree, which is logarithmic in the number of
attributes. We also prove that computing the LP tree that minimises the
empirical risk can be done in polynomial time when restricted to the class of
linear LP-trees. |
| doi_str_mv | 10.48550/arxiv.2209.11505 |
| format | Article |
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Handling, Jul 2022, Vienne, Austria This paper considers the task of learning users' preferences on a
combinatorial set of alternatives, as generally used by online configurators,
for example. In many settings, only a set of selected alternatives during past
interactions is available to the learner. Fargier et al. [2018] propose an
approach to learn, in such a setting, a model of the users' preferences that
ranks previously chosen alternatives as high as possible; and an algorithm to
learn, in this setting, a particular model of preferences: lexicographic
preferences trees (LP-trees). In this paper, we study complexity-theoretical
problems related to this approach. We give an upper bound on the sample
complexity of learning an LP-tree, which is logarithmic in the number of
attributes. We also prove that computing the LP tree that minimises the
empirical risk can be done in polynomial time when restricted to the class of
linear LP-trees.</description><identifier>DOI: 10.48550/arxiv.2209.11505</identifier><language>eng</language><subject>Computer Science - Artificial Intelligence ; Computer Science - Computational Complexity ; Computer Science - Learning</subject><creationdate>2022-09</creationdate><rights>http://arxiv.org/licenses/nonexclusive-distrib/1.0</rights><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,776,881</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/2209.11505$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.2209.11505$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Fargier, Hélène</creatorcontrib><creatorcontrib>Gimenez, Pierre-François</creatorcontrib><creatorcontrib>Mengin, Jérôme</creatorcontrib><creatorcontrib>Nguyen, Bao Ngoc Le</creatorcontrib><title>The complexity of unsupervised learning of lexicographic preferences</title><description>13th Multidisciplinary Workshop on Advances in Preference
Handling, Jul 2022, Vienne, Austria This paper considers the task of learning users' preferences on a
combinatorial set of alternatives, as generally used by online configurators,
for example. In many settings, only a set of selected alternatives during past
interactions is available to the learner. Fargier et al. [2018] propose an
approach to learn, in such a setting, a model of the users' preferences that
ranks previously chosen alternatives as high as possible; and an algorithm to
learn, in this setting, a particular model of preferences: lexicographic
preferences trees (LP-trees). In this paper, we study complexity-theoretical
problems related to this approach. We give an upper bound on the sample
complexity of learning an LP-tree, which is logarithmic in the number of
attributes. We also prove that computing the LP tree that minimises the
empirical risk can be done in polynomial time when restricted to the class of
linear LP-trees.</description><subject>Computer Science - Artificial Intelligence</subject><subject>Computer Science - Computational Complexity</subject><subject>Computer Science - Learning</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2022</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotj7FOwzAURb10QIUPYMI_kODYfqk9otICUiWW7NGL_dxaShPLaav27yGF4eoO9-hKh7HnSpTaAIhXzNd4KaUUtqwqEPDA3psDcTceU0_XeLrxMfDzMJ0T5UucyPOeMA9x2M_DjLhxnzEdouMpU6BMg6PpkS0C9hM9_feSNdtNs_4sdt8fX-u3XYH1CgoLSmtVBxuIgtakVtKDkgKR3G8sBGVkJ4QxApTxGrCz0huUXlDdOaOW7OXv9q7RphyPmG_trNPeddQPAcpGXg</recordid><startdate>20220923</startdate><enddate>20220923</enddate><creator>Fargier, Hélène</creator><creator>Gimenez, Pierre-François</creator><creator>Mengin, Jérôme</creator><creator>Nguyen, Bao Ngoc Le</creator><scope>AKY</scope><scope>GOX</scope></search><sort><creationdate>20220923</creationdate><title>The complexity of unsupervised learning of lexicographic preferences</title><author>Fargier, Hélène ; Gimenez, Pierre-François ; Mengin, Jérôme ; Nguyen, Bao Ngoc Le</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a675-9534436f9feef44e372d5320aaecaae95f382b00880538d45ab92d8a2d0e6bc83</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2022</creationdate><topic>Computer Science - Artificial Intelligence</topic><topic>Computer Science - Computational Complexity</topic><topic>Computer Science - Learning</topic><toplevel>online_resources</toplevel><creatorcontrib>Fargier, Hélène</creatorcontrib><creatorcontrib>Gimenez, Pierre-François</creatorcontrib><creatorcontrib>Mengin, Jérôme</creatorcontrib><creatorcontrib>Nguyen, Bao Ngoc Le</creatorcontrib><collection>arXiv Computer Science</collection><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Fargier, Hélène</au><au>Gimenez, Pierre-François</au><au>Mengin, Jérôme</au><au>Nguyen, Bao Ngoc Le</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The complexity of unsupervised learning of lexicographic preferences</atitle><date>2022-09-23</date><risdate>2022</risdate><abstract>13th Multidisciplinary Workshop on Advances in Preference
Handling, Jul 2022, Vienne, Austria This paper considers the task of learning users' preferences on a
combinatorial set of alternatives, as generally used by online configurators,
for example. In many settings, only a set of selected alternatives during past
interactions is available to the learner. Fargier et al. [2018] propose an
approach to learn, in such a setting, a model of the users' preferences that
ranks previously chosen alternatives as high as possible; and an algorithm to
learn, in this setting, a particular model of preferences: lexicographic
preferences trees (LP-trees). In this paper, we study complexity-theoretical
problems related to this approach. We give an upper bound on the sample
complexity of learning an LP-tree, which is logarithmic in the number of
attributes. We also prove that computing the LP tree that minimises the
empirical risk can be done in polynomial time when restricted to the class of
linear LP-trees.</abstract><doi>10.48550/arxiv.2209.11505</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Computer Science - Artificial Intelligence Computer Science - Computational Complexity Computer Science - Learning |
| title | The complexity of unsupervised learning of lexicographic preferences |
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