{"id":9611,"date":"2026-01-09T07:02:32","date_gmt":"2026-01-09T07:02:32","guid":{"rendered":"https:\/\/mailitics.com\/index.php\/2026\/01\/09\/2601-04423\/"},"modified":"2026-01-09T07:02:32","modified_gmt":"2026-01-09T07:02:32","slug":"2601-04423","status":"publish","type":"post","link":"https:\/\/mailitics.com\/index.php\/2026\/01\/09\/2601-04423\/","title":{"rendered":"Learning Multinomial Logits in $O(n log n)$ time"},"content":{"rendered":"

Learning Multinomial Logits in $O(n log n)$ time
\n \t

\n
<\/BR>
\n
\n \t

\n
<\/BR><\/p>\n

arXiv:2601.04423v1 Announce Type: cross
\nAbstract: A Multinomial Logit (MNL) model is composed of a finite universe of items $[n]={1,…, n}$, each assigned a positive weight. A query specifies an admissible subset — called a slate — and the model chooses one item from that slate with probability proportional to its weight. This query model is also known as the Plackett-Luce model or conditional sampling oracle in the literature. Although MNLs have been studied extensively, a basic computational question remains open: given query access to slates, how efficiently can we learn weights so that, for every slate, the induced choice distribution is within total variation distance $varepsilon$ of the ground truth? This question is central to MNL learning and has direct implications for modern recommender system interfaces.
\n We provide two algorithms for this task, one with adaptive queries and one with non-adaptive queries. Each algorithm outputs an MNL $M’$ that induces, for each slate $S$, a distribution $M’_S$ on $S$ that is within $varepsilon$ total variation distance of the true distribution. Our adaptive algorithm makes $Oleft(frac{n}{varepsilon^{3}}log nright)$ queries, while our non-adaptive algorithm makes $Oleft(frac{n^{2}}{varepsilon^{3}}log n logfrac{n}{varepsilon}right)$ queries. Both algorithms query only slates of size two and run in time proportional to their query complexity.
\n We complement these upper bounds with lower bounds of $Omegaleft(frac{n}{varepsilon^{2}}log nright)$ for adaptive queries and $Omegaleft(frac{n^{2}}{varepsilon^{2}}log nright)$ for non-adaptive queries, thus proving that our adaptive algorithm is optimal in its dependence on the support size $n$, while the non-adaptive one is tight within a $log n$ factor.<\/div>\n

\t

\n
<\/BR>
\n Flavio Chierichetti, Mirko Giacchini, Ravi Kumar, Silvio Lattanzi, Alessandro Panconesi, Erasmo Tani, Andrew Tomkins
\n \t

\n
<\/BR>
\nGo to original source<\/a>
\n \t

\n
<\/BR><\/p>\n","protected":false},"excerpt":{"rendered":"

Learning Multinomial Logits in $O(n log n)$ time arXiv:2601.04423v1 Announce Type: cross Abstract: A Multinomial Logit (MNL) model is composed of a finite universe of items $[n]={1,…, n}$, each assigned a positive weight. A query specifies an admissible subset — called a slate — and the model chooses one item from that slate with probability […]<\/p>\n","protected":false},"author":2,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[62,413,113,190,112,191],"tags":[1021,1148,2953],"class_list":["post-9611","post","type-post","status-publish","format-standard","hentry","category-aimldsaimlds","category-cs-ds","category-cs-lg","category-math-st","category-stat-ml","category-stat-th","tag-adaptive","tag-log","tag-varepsilon"],"_links":{"self":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9611"}],"collection":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/users\/2"}],"replies":[{"embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/comments?post=9611"}],"version-history":[{"count":0,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/posts\/9611\/revisions"}],"wp:attachment":[{"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/media?parent=9611"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/categories?post=9611"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mailitics.com\/index.php\/wp-json\/wp\/v2\/tags?post=9611"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}