{"id":5593,"date":"2020-07-20T08:09:52","date_gmt":"2020-07-20T07:09:52","guid":{"rendered":"https:\/\/datascientest.com\/?p=5593"},"modified":"2024-09-21T10:46:01","modified_gmt":"2024-09-21T10:46:01","slug":"descente-de-gradient","status":"publish","type":"post","link":"https:\/\/datascientest.com\/descente-de-gradient","title":{"rendered":"Algorithme de descente de gradient : Qu&rsquo;est-ce que c&rsquo;est ?"},"content":{"rendered":"\t\t<div data-elementor-type=\"wp-post\" data-elementor-id=\"5593\" class=\"elementor elementor-5593\" data-elementor-post-type=\"post\">\n\t\t\t\t\t\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-58d3a16 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"58d3a16\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-8ddd1de\" data-id=\"8ddd1de\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c57569c elementor-widget elementor-widget-text-editor\" data-id=\"c57569c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-text-editor.elementor-drop-cap-view-stacked .elementor-drop-cap{background-color:#69727d;color:#fff}.elementor-widget-text-editor.elementor-drop-cap-view-framed .elementor-drop-cap{color:#69727d;border:3px solid;background-color:transparent}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap{margin-top:8px}.elementor-widget-text-editor:not(.elementor-drop-cap-view-default) .elementor-drop-cap-letter{width:1em;height:1em}.elementor-widget-text-editor .elementor-drop-cap{float:left;text-align:center;line-height:1;font-size:50px}.elementor-widget-text-editor .elementor-drop-cap-letter{display:inline-block}<\/style>\t\t\t\t<h2>Beaucoup d\u2019algorithmes de Machine Learning obtiennent de bonnes performances gr\u00e2ce \u00e0 leur entra\u00eenement. Cependant, une grande majorit\u00e9 des entra\u00eenements repose sur l\u2019optimisation d\u2019une fonction de perte. Plus sa valeur est petite, meilleurs sont les r\u00e9sultats de l\u2019algorithme. Ainsi, l\u2019algorithme de descente de gradient est un des nombreux moyens qui permettent de trouver le minimum (ou maximum) d\u2019une fonction.<\/h2>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-89a60e2 elementor-widget elementor-widget-text-editor\" data-id=\"89a60e2\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Une premi\u00e8re approche intuitive de cet algorithme a \u00e9t\u00e9 donn\u00e9e dans\u00a0<a href=\"https:\/\/datascientest.com\/deep_learning#fonctionnement\">cet article<\/a>.<\/p><p>Ici, nous allons revenir sur les fondements math\u00e9matiques de cet algorithme, l\u2019importance du taux d\u2019apprentissage.<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-7c30c90 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"7c30c90\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-00e47bf\" data-id=\"00e47bf\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-614cd81 elementor-widget elementor-widget-heading\" data-id=\"614cd81\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-heading-title{padding:0;margin:0;line-height:1}.elementor-widget-heading .elementor-heading-title[class*=elementor-size-]>a{color:inherit;font-size:inherit;line-height:inherit}.elementor-widget-heading .elementor-heading-title.elementor-size-small{font-size:15px}.elementor-widget-heading .elementor-heading-title.elementor-size-medium{font-size:19px}.elementor-widget-heading .elementor-heading-title.elementor-size-large{font-size:29px}.elementor-widget-heading .elementor-heading-title.elementor-size-xl{font-size:39px}.elementor-widget-heading .elementor-heading-title.elementor-size-xxl{font-size:59px}<\/style><h3 class=\"elementor-heading-title elementor-size-default\">Descente du gradient : Formalisation math\u00e9matiques<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-4042e06 elementor-widget elementor-widget-text-editor\" data-id=\"4042e06\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">La descente du gradient est un des nombreux algorithmes dits de descente. La formule g\u00e9n\u00e9rale est la suivante\u00a0:\u00a0<\/span><\/p><p style=\"text-align: center;\"><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t+1<\/sub><\/span><span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t<\/sub><\/span><span style=\"font-weight: 400;\">&#8211; \u03b7\u2206<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t<\/sub><\/span><\/p><p><span style=\"font-weight: 400;\">o\u00f9 \u03b7\u00a0<\/span> <b>le taux d\u2019apprentissage<\/b><span style=\"font-weight: 400;\"> et <\/span><span style=\"font-weight: 400;\">\u2206<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t<\/sub><\/span> <b>la direction de descente<\/b><span style=\"font-weight: 400;\">. Cette classe d\u2019algorithme a pour but \u00e0 chaque it\u00e9ration d\u2019avoir \u0192(<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t+1<\/sub>) <\/span><span style=\"font-weight: 400;\">\u2264 \u0192 (<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t<\/sub>)<\/span><span style=\"font-weight: 400;\"> , avec \u0192<\/span><span style=\"font-weight: 400;\">\u00a0une <\/span><b>fonction convexe<\/b><span style=\"font-weight: 400;\"> que l\u2019on souhaite minimiser.<\/span><\/p><p><span style=\"font-weight: 400;\">L\u2019algorithme de descente du gradient d\u00e9cide de suivre comme direction de descente l\u2019oppos\u00e9 du gradient d\u2019une fonction <\/span><b>convexe<\/b><span style=\"font-weight: 400;\"> f, ie <\/span><span style=\"font-weight: 400;\">&#8211; \u0394<\/span><span style=\"font-weight: 400;\">\u0192 <\/span><span style=\"font-weight: 400;\">. <\/span><\/p><p><span style=\"font-weight: 400;\">Pourquoi ? Le gradient d\u2019une fonction indique sa croissance maximale \u00e0 partir d\u2019un point. Alors choisir l\u2019oppos\u00e9 revient \u00e0 prendre la pente la plus abrupte, dans l\u2019objectif de minimiser la valeur de cette fonction.\u00a0 Voici son fonctionnement :<\/span><\/p><ol><li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">\u00a0Soit un point d\u2019initialisation <\/span><span style=\"font-weight: 400;\">x<sub>0<\/sub><\/span><span style=\"font-weight: 400;\"> appartenant au domaine de <\/span><span style=\"font-weight: 400;\">f<\/span><\/li><li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Calculer <\/span><span style=\"font-weight: 400;\">f(<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t<\/sub><\/span><span style=\"font-weight: 400;\">)<\/span><\/li><li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">Mettre \u00e0 jour les coordonn\u00e9es\u00a0: <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t+1 <\/sub><\/span><span style=\"font-weight: 400;\">= <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t<\/sub><\/span><span style=\"font-weight: 400;\">&#8211; \u03b7 \u0394 <\/span><span style=\"font-weight: 400;\">\u0192 (<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t<\/sub><\/span><span style=\"font-weight: 400;\"> )\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0(*)<\/span><\/li><li style=\"font-weight: 400;\"><span style=\"font-weight: 400;\">R\u00e9p\u00e9ter 2 et 3 jusqu\u2019au crit\u00e8re d\u2019arr\u00eat<\/span><\/li><\/ol><p><span style=\"font-weight: 400;\">G\u00e9n\u00e9ralement, le crit\u00e8re d\u2019arr\u00eat est de la forme <\/span><span style=\"font-weight: 400;\">|\u0192<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t+1 <\/sub><\/span><span style=\"font-weight: 400;\">&#8211; \u0192<\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>t<\/sub><\/span><span style=\"font-weight: 400;\">| \u2264 \u03b5<\/span><span style=\"font-weight: 400;\"> , o\u00f9 <\/span><span style=\"font-weight: 400;\"> est tr\u00e8s petit. Ce crit\u00e8re semble logique puisqu\u2019on d\u00e9cide d\u2019arr\u00eater quand la diff\u00e9rence entre les valeurs de la fonction prise en deux points diff\u00e9rents est tr\u00e8s peu significative, signe qu\u2019on a converg\u00e9. Un crit\u00e8re d\u2019arr\u00eat reconnu dans le machine learning est celui du nombre d\u2019it\u00e9rations\u00a0; on r\u00e9alise un nombre fini d\u2019optimisation (\u00e9tape 2 et 3).<\/span><\/p><p><span style=\"font-weight: 400;\">Deux \u00e9l\u00e9ments, \u00e0 priori n\u00e9gligeables quand on regarde l\u2019algorithme, sont en r\u00e9alit\u00e9 cruciaux pour le bon fonctionnement de ce dernier\u00a0; le point d\u2019initialisation <\/span><span style=\"font-weight: 400;\">x<\/span><span style=\"font-weight: 400;\"><sub>0<\/sub><\/span> <span style=\"font-weight: 400;\">et la valeur du taux d\u2019apprentissage \u03b7<\/span><span style=\"font-weight: 400;\">. <\/span><b>Un mauvais point d\u2019initialisation ou un taux d\u2019apprentissage peu adapt\u00e9 peut emp\u00eacher l\u2019algorithme de converger vers le minimum<\/b><span style=\"font-weight: 400;\">. Plus le taux d\u2019apprentissage est \u00e9lev\u00e9, plus on suivra loin la direction indiqu\u00e9e par le gradient. Cela peut nous bloquer dans un minimum local, sur un point-selle o\u00f9 nous faire louper le minimum global. Nous allons \u00e9tudier \u00e0 travers un exemple simple\u00a0 l\u2019impact du taux d\u2019apprentissage sur les performances de la descente de gradient.<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-53aabc4 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"53aabc4\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-badd640\" data-id=\"badd640\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-7071bf2 elementor-widget elementor-widget-heading\" data-id=\"7071bf2\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Importance du taux d\u2019apprentissage\n<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-97eb31f elementor-widget elementor-widget-text-editor\" data-id=\"97eb31f\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Prenons le cas d\u2019un exemple simple de r\u00e9gression lin\u00e9aire. Soit une droite y=w<sub>0<\/sub>*x+w<sub>1<\/sub>. Nous avons n observations qui suivent une relation lin\u00e9aire et \u00e0 l\u2019aide de ces celles-ci, <strong>nous allons tenter de trouver les bons param\u00e8tres<\/strong>, w<sub>0 <\/sub>et w<sub>1<\/sub>, qui d\u00e9finissent cette relation. Comme dit pr\u00e9c\u00e9demment, optimiser un mod\u00e8le, c\u2019est-\u00e0-dire <strong>trouver les meilleurs param\u00e8tres<\/strong> permettant de bonnes performances, revient \u00e0 <strong>optimiser une fonction de perte<\/strong>. La fonction de perte qui s\u2019impose dans ce genre de situation est la <strong>MSE<\/strong>,<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-cb44d99 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"cb44d99\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5eff56e\" data-id=\"5eff56e\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5488cd4 elementor-widget elementor-widget-image\" data-id=\"5488cd4\" data-element_type=\"widget\" data-widget_type=\"image.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-image{text-align:center}.elementor-widget-image a{display:inline-block}.elementor-widget-image a img[src$=\".svg\"]{width:48px}.elementor-widget-image img{vertical-align:middle;display:inline-block}<\/style>\t\t\t\t\t\t\t\t\t\t\t\t<img decoding=\"async\" width=\"768\" height=\"120\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/07\/Capture-d\u2019e\u0301cran-2020-07-13-a\u0300-16.25.35.png\" class=\"attachment-large size-large wp-image-5604\" alt=\"gradient\" loading=\"lazy\" srcset=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/07\/Capture-d\u2019e\u0301cran-2020-07-13-a\u0300-16.25.35.png 768w, https:\/\/datascientest.com\/wp-content\/uploads\/2020\/07\/Capture-d\u2019e\u0301cran-2020-07-13-a\u0300-16.25.35-300x47.png 300w\" sizes=\"(max-width: 768px) 100vw, 768px\" \/>\t\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-4bade70 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"4bade70\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ce87137\" data-id=\"ce87137\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-f72f693 elementor-widget elementor-widget-text-editor\" data-id=\"f72f693\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\to\u00f9 t repr\u00e9sente la t<sup>i\u00e8me <\/sup>it\u00e9ration.\n\nEn calculant le gradient de cette fonction et en appliquant la formule (*), on obtient la formule de mise \u00e0 jour des param\u00e8tres :\n\n\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-6ac7490 elementor-widget elementor-widget-text-editor\" data-id=\"6ac7490\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p style=\"text-align: center;\">w<sub>t+1,0<\/sub> w<sub>t+1, 1 <\/sub> = w<sub>t,1<\/sub>&#8211; \u03b7\u0394<sub>w1<\/sub>L(w<sub>t,0<\/sub>, w<sub>t,1<\/sub>, X) w<sub>t,2 <\/sub>&#8211; \u03b7\u0394<sub>w2<\/sub>L(w<sub>t,0<\/sub>, w<sub>t,1<\/sub>, X)<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-1976601 elementor-widget elementor-widget-text-editor\" data-id=\"1976601\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Au niveau code, cela donne le r\u00e9sultat suivant\u00a0:\u00a0<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-04069d9 elementor-widget elementor-widget-shortcode\" data-id=\"04069d9\" data-element_type=\"widget\" data-widget_type=\"shortcode.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"elementor-shortcode\"><script src=\u201chttps:\/\/gist.github.com\/guipet\/b17f9c69c6058869ea412c05e14a2e9c.js\u201d><\/script><\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1413586 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1413586\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-d7a58d5\" data-id=\"d7a58d5\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c6d28f7 elementor-widget elementor-widget-text-editor\" data-id=\"c6d28f7\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Faisons varier le taux d\u2019apprentissage pour observer son impact sur les performances du mod\u00e8le, le tout sur plus de 100 it\u00e9rations.\u00a0<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-811f3d9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"811f3d9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c004c47\" data-id=\"c004c47\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-5a610af elementor-widget elementor-widget-heading\" data-id=\"5a610af\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Un petit taux d\u2019apprentissage ?<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-2aa48da elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"2aa48da\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-318e0dc\" data-id=\"318e0dc\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ae4d8bf elementor-widget elementor-widget-text-editor\" data-id=\"ae4d8bf\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-size: 17px; font-weight: 400;\">Prenons un pas volontairement petit de 0.01 pour commencer.\u00a0 On remarque que le mod\u00e8le met beaucoup de temps \u00e0 converger. Apr\u00e8s 100 it\u00e9rations, on voit \u00e0 peine le mod\u00e8le approximer les observations.\u00a0<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-8a2ef99 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"8a2ef99\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6ed3aec\" data-id=\"6ed3aec\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-554ec63 elementor-widget elementor-widget-video\" data-id=\"554ec63\" data-element_type=\"widget\" data-settings=\"{&quot;video_type&quot;:&quot;hosted&quot;,&quot;controls&quot;:&quot;yes&quot;}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<style>\/*! elementor - v3.15.0 - 02-08-2023 *\/\n.elementor-widget-video .elementor-widget-container{overflow:hidden;transform:translateZ(0)}.elementor-widget-video .elementor-wrapper{aspect-ratio:var(--video-aspect-ratio)}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{height:100%;width:100%;display:flex;border:none;background-color:#000}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-wrapper{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-wrapper iframe,.elementor-widget-video .elementor-wrapper video{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .elementor-open-inline .elementor-custom-embed-image-overlay{position:absolute;top:0;right:0;bottom:0;left:0;background-size:cover;background-position:50%}.elementor-widget-video .elementor-custom-embed-image-overlay{cursor:pointer;text-align:center}.elementor-widget-video .elementor-custom-embed-image-overlay:hover .elementor-custom-embed-play i{opacity:1}.elementor-widget-video .elementor-custom-embed-image-overlay img{display:block;width:100%;aspect-ratio:var(--video-aspect-ratio);-o-object-fit:cover;object-fit:cover;-o-object-position:center center;object-position:center center}@supports not (aspect-ratio:1\/1){.elementor-widget-video .elementor-custom-embed-image-overlay{position:relative;overflow:hidden;height:0;padding-bottom:calc(100% \/ var(--video-aspect-ratio))}.elementor-widget-video .elementor-custom-embed-image-overlay img{position:absolute;top:0;right:0;bottom:0;left:0}}.elementor-widget-video .e-hosted-video .elementor-video{-o-object-fit:cover;object-fit:cover}.e-con-inner>.elementor-widget-video,.e-con>.elementor-widget-video{width:var(--container-widget-width);--flex-grow:var(--container-widget-flex-grow)}<\/style>\t\t<div class=\"e-hosted-video elementor-wrapper elementor-open-inline\">\n\t\t\t\t\t<video class=\"elementor-video\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/07\/Trop-lent.mov\" controls=\"\" preload=\"metadata\" controlsList=\"nodownload\"><\/video>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-a238ec2 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"a238ec2\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-b510ff9\" data-id=\"b510ff9\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-2bca2ce elementor-widget elementor-widget-text-editor\" data-id=\"2bca2ce\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<span style=\"font-weight: 400;\">On peut d\u2019ailleurs observer sur le troisi\u00e8me graphique que le param\u00e8tre <\/span><span style=\"font-weight: 400;\">w<\/span><span style=\"font-weight: 400;\"><sub>1<\/sub><\/span><span style=\"font-weight: 400;\"> varie beaucoup au cours de l\u2019optimisation. Le dernier graphique nous r\u00e9v\u00e8le la lenteur de la variation de la fonction de perte vers son minimum global.\u00a0 <\/span><b>Cela est le signe que le taux d\u2019apprentissage est trop petit. <\/b><span style=\"font-weight: 400;\">Varions-le vers 0.99.<\/span>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-47c1bfc elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"47c1bfc\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-6b31aa3\" data-id=\"6b31aa3\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-34bef19 elementor-widget elementor-widget-heading\" data-id=\"34bef19\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Un grand taux d\u2019apprentissage ?\n<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-3d64f32 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"3d64f32\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2985311\" data-id=\"2985311\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-759a96b elementor-widget elementor-widget-video\" data-id=\"759a96b\" data-element_type=\"widget\" data-settings=\"{&quot;video_type&quot;:&quot;hosted&quot;,&quot;show_image_overlay&quot;:&quot;yes&quot;,&quot;controls&quot;:&quot;yes&quot;,&quot;image_overlay&quot;:{&quot;url&quot;:&quot;https:\\\/\\\/datascientest.com\\\/wp-content\\\/plugins\\\/elementor\\\/assets\\\/images\\\/placeholder.png&quot;,&quot;id&quot;:&quot;&quot;,&quot;size&quot;:&quot;&quot;}}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"e-hosted-video elementor-wrapper elementor-open-inline\">\n\t\t\t\t\t<video class=\"elementor-video\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/07\/Trop-grand.mov\" controls=\"\" preload=\"metadata\" controlsList=\"nodownload\"><\/video>\n\t\t\t\t\t\t<div class=\"elementor-custom-embed-image-overlay\" style=\"background-image: url(https:\/\/datascientest.com\/wp-content\/plugins\/elementor\/assets\/images\/placeholder.png);\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-ebe3dae elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"ebe3dae\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a10287a\" data-id=\"a10287a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-6d384bc elementor-widget elementor-widget-text-editor\" data-id=\"6d384bc\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<span style=\"font-weight: 400;\">Analysons graphique par graphique. Le 1<\/span><span style=\"font-weight: 400;\">er<\/span><span style=\"font-weight: 400;\"> graphique montre une grande instabilit\u00e9 de l\u2019approximation lin\u00e9aire. On remarque qu\u2019elle au-dessus et en dessous. Cela s\u2019explique par la variation instable et brutale de <\/span><span style=\"font-weight: 400;\">w<\/span><span style=\"font-weight: 400;\"><sub>1<\/sub><\/span><span style=\"font-weight: 400;\"> sur le 3<\/span><span style=\"font-weight: 400;\">\u00e8me<\/span><span style=\"font-weight: 400;\"> graphique, responsable de la \u00ab\u00a0hauteur\u00a0\u00bb de la droite sur le plan. D\u2019o\u00f9 provient cette instabilit\u00e9\u00a0? La r\u00e9ponse se trouve sur le 4<\/span><span style=\"font-weight: 400;\">\u00e8me<\/span><span style=\"font-weight: 400;\"> graphique.\u00a0<\/span>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-982a6e3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"982a6e3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ce6a17b\" data-id=\"ce6a17b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-ffd49e8 elementor-widget elementor-widget-text-editor\" data-id=\"ffd49e8\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<span style=\"font-weight: 400;\">Le taux \u00e9lev\u00e9 fait jouer \u00e0 la perte une sorte d\u2019effet de ping-pong entre les deux versants sur l\u2019axe de w<sub>1<\/sub> . Cet effet ping-pong ralentit la diminution de la valeur de notre fonction de perte.\u00a0<\/span>\n\n<span style=\"font-weight: 400;\">D\u2019ailleurs sur le second graphique, on voit que la valeur de notre perte reste longtemps \u00e9lev\u00e9e au cours des it\u00e9rations puisqu\u2019elle n\u2019appara\u00eet m\u00eame pas sur le graphique pendant la moiti\u00e9 du temps. L\u2019intuition nous indique qu\u2019il faudrait le diminuer.\u00a0 Diminuons donc le taux \u00e0 0.7 et observons le r\u00e9sultat.\u00a0<\/span>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-628d48c elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"628d48c\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-c3da35c\" data-id=\"c3da35c\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c111e8c elementor-widget elementor-widget-heading\" data-id=\"c111e8c\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">Un taux plus adapt\u00e9<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6df0bc3 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6df0bc3\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-3851959\" data-id=\"3851959\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-493198b elementor-widget elementor-widget-text-editor\" data-id=\"493198b\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Ce taux d\u2019apprentissage semble \u00eatre optimal. On remarque sur le dernier graphique que d\u00e8s la premi\u00e8re it\u00e9ration, la valeur de la fonction de perte diminue drastiquement, comme cela est indiqu\u00e9 sur le second graphique. Arriv\u00e9 au creux de la fonction, l\u2019algorithme se stabilise assez rapidement au minimum\u00a0vers la dixi\u00e8me \u00e9poque\u00a0: le mod\u00e8le approxime parfaitement les donn\u00e9es, la fonction de perte se stabilise en 0, son minimum global, et les param\u00e8tres sur le graphique 3 stagnes car optimaux\u00a0!\u00a0<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-6e49abb elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"6e49abb\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-a449f25\" data-id=\"a449f25\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-0dac331 elementor-widget elementor-widget-video\" data-id=\"0dac331\" data-element_type=\"widget\" data-settings=\"{&quot;video_type&quot;:&quot;hosted&quot;,&quot;show_image_overlay&quot;:&quot;yes&quot;,&quot;controls&quot;:&quot;yes&quot;,&quot;image_overlay&quot;:{&quot;url&quot;:&quot;https:\\\/\\\/datascientest.com\\\/wp-content\\\/plugins\\\/elementor\\\/assets\\\/images\\\/placeholder.png&quot;,&quot;id&quot;:&quot;&quot;,&quot;size&quot;:&quot;&quot;}}\" data-widget_type=\"video.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t<div class=\"e-hosted-video elementor-wrapper elementor-open-inline\">\n\t\t\t\t\t<video class=\"elementor-video\" src=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/07\/Parfait.mov\" controls=\"\" preload=\"metadata\" controlsList=\"nodownload\"><\/video>\n\t\t\t\t\t\t<div class=\"elementor-custom-embed-image-overlay\" style=\"background-image: url(https:\/\/datascientest.com\/wp-content\/plugins\/elementor\/assets\/images\/placeholder.png);\">\n\t\t\t\t\t\t\t\t\t\t\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-1894df9 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"1894df9\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-5b00a7a\" data-id=\"5b00a7a\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-caee30f elementor-widget elementor-widget-heading\" data-id=\"caee30f\" data-element_type=\"widget\" data-widget_type=\"heading.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t<h3 class=\"elementor-heading-title elementor-size-default\">La complexit\u00e9 du taux d\u2019apprentissage\n<\/h3>\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-e4ed6ee elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"e4ed6ee\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-ff1cf9b\" data-id=\"ff1cf9b\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-c2ba042 elementor-widget elementor-widget-text-editor\" data-id=\"c2ba042\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Nous avons observ\u00e9 que le taux d\u2019apprentissage joue un r\u00f4le crucial. S\u2019il est trop \u00e9lev\u00e9, on peut osciller tr\u00e8s longtemps autour du minimum, voir le manquer, tandis qu\u2019un taux d\u2019apprentissage trop petit peu mettre beaucoup de temps avant de converger. Un taux m\u00eame trop \u00e9lev\u00e9 peut faire diverger et aller \u00e0 l\u2019encontre du but voulu, i.e. atteindre le minimum. Le probl\u00e8me est le m\u00eame pour le point d\u2019initialisation. Deux points d\u2019initialisation peuvent mener \u00e0 deux r\u00e9sultats diff\u00e9rents en fonction de la complexit\u00e9 de la fonction de perte.\u00a0<\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t<div class=\"elementor-element elementor-element-c29b0f1 elementor-widget elementor-widget-text-editor\" data-id=\"c29b0f1\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p><span style=\"font-weight: 400;\">Ici, nous \u00e9tions dans un mod\u00e8le simple, avec deux param\u00e8tres, ce qui nous a permis de visualiser l\u2019\u00e9volution du mod\u00e8le. Dans les faits, notre mod\u00e8le comporte bien plus de param\u00e8tres, rendant la visualisation impossible. Alors l\u2019ajustement du taux d\u2019apprentissage et le choix du point d\u2019initialisation sont beaucoup plus compliqu\u00e9s dans la r\u00e9alit\u00e9. Dans la pratique, il n\u00e9cessaire d\u2019appliquer \u00e0 note mod\u00e8le divers taux d\u2019apprentissage pour observer celui qui apporte les meilleures performances, de m\u00eame pour le point d\u2019initialisation.\u00a0 <\/span><\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t<section class=\"elementor-section elementor-top-section elementor-element elementor-element-5f98168 elementor-section-boxed elementor-section-height-default elementor-section-height-default\" data-id=\"5f98168\" data-element_type=\"section\">\n\t\t\t\t\t\t<div class=\"elementor-container elementor-column-gap-default\">\n\t\t\t\t\t<div class=\"elementor-column elementor-col-100 elementor-top-column elementor-element elementor-element-2e8e927\" data-id=\"2e8e927\" data-element_type=\"column\">\n\t\t\t<div class=\"elementor-widget-wrap elementor-element-populated\">\n\t\t\t\t\t\t\t\t<div class=\"elementor-element elementor-element-e14b76c elementor-widget elementor-widget-text-editor\" data-id=\"e14b76c\" data-element_type=\"widget\" data-widget_type=\"text-editor.default\">\n\t\t\t\t<div class=\"elementor-widget-container\">\n\t\t\t\t\t\t\t<p>Cet article vous a plu ?<a href=\"https:\/\/6fdb24d0.sibforms.com\/serve\/MUIEAK6UnrbR236UIB9QygO2ap6AQtaii7bMdnFUBKwbvV7knWSCcYwRdisgEXpe-qT7m-GT0as6Fh7JpaLdiwD0_5Cep5Ps3qEScmsvKrZh6NymnqcSrSFpJNirHNaUlqRAXBosIGGdsaWj1pYFbrgisoTFC0bnBnpW5x8XX4azcIPeA7PGuo-f-22EQgqvnjipuXZ4W9nU8ext\" target=\"_blank\" rel=\"noopener\"> Inscrivez vous \u00e0 notre Newsletter<\/a>\u00a0pour en recevoir d&rsquo;autres r\u00e9guli\u00e8rement !\u00a0<\/p>\t\t\t\t\t\t<\/div>\n\t\t\t\t<\/div>\n\t\t\t\t\t<\/div>\n\t\t<\/div>\n\t\t\t\t\t\t\t<\/div>\n\t\t<\/section>\n\t\t\t\t\t\t\t<\/div>\n\t\t","protected":false},"excerpt":{"rendered":"<p>Beaucoup d\u2019algorithmes de Machine Learning obtiennent de bonnes performances gr\u00e2ce \u00e0 leur entra\u00eenement. Cependant, une grande majorit\u00e9 des entra\u00eenements repose sur l\u2019optimisation d\u2019une fonction de perte. Plus sa valeur est petite, meilleurs sont les r\u00e9sultats de l\u2019algorithme. Ainsi, l\u2019algorithme de descente de gradient est un des nombreux moyens qui permettent de trouver le minimum (ou [&hellip;]<\/p>\n","protected":false},"author":78,"featured_media":6033,"comment_status":"open","ping_status":"open","sticky":false,"template":"elementor_theme","format":"standard","meta":{"content-type":"","inline_featured_image":false},"categories":[2497],"tags":[],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v21.7 (Yoast SEO v21.7) - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>Algorithme de descente de gradient : Qu&#039;est-ce que c&#039;est ?<\/title>\n<meta name=\"description\" content=\"C\u00e9l\u00e8bre algorithme de Machine Learning, d\u00e9couvrez dans cet article les math\u00e9matiques qui se cachent derri\u00e8re la descente de gradient !\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/datascientest.com\/descente-de-gradient\" \/>\n<meta property=\"og:locale\" content=\"fr_FR\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Algorithme de descente de gradient : Qu&#039;est-ce que c&#039;est ?\" \/>\n<meta property=\"og:url\" content=\"https:\/\/datascientest.com\/descente-de-gradient\" \/>\n<meta property=\"og:site_name\" content=\"Formation Data Science | DataScientest.com\" \/>\n<meta property=\"article:published_time\" content=\"2020-07-20T07:09:52+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2024-09-21T10:46:01+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/datascientest.com\/wp-content\/uploads\/2020\/07\/black-and-white-blur-book-business-240163-scaled.jpg\" \/>\n\t<meta property=\"og:image:width\" content=\"2560\" \/>\n\t<meta property=\"og:image:height\" content=\"1440\" \/>\n\t<meta property=\"og:image:type\" content=\"image\/jpeg\" \/>\n<meta name=\"author\" content=\"J\u00e9r\u00e9my Robert\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"\u00c9crit par\" \/>\n\t<meta name=\"twitter:data1\" content=\"J\u00e9r\u00e9my Robert\" \/>\n\t<meta name=\"twitter:label2\" content=\"Dur\u00e9e de lecture estim\u00e9e\" \/>\n\t<meta name=\"twitter:data2\" content=\"7 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"WebPage\",\"@id\":\"https:\/\/datascientest.com\/descente-de-gradient\",\"url\":\"https:\/\/datascientest.com\/descente-de-gradient\",\"name\":\"Algorithme de descente de gradient : Qu'est-ce que c'est ?\",\"isPartOf\":{\"@id\":\"https:\/\/datascientest.com\/#website\"},\"datePublished\":\"2020-07-20T07:09:52+00:00\",\"dateModified\":\"2024-09-21T10:46:01+00:00\",\"author\":{\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/7af2361c48e24e79a8aa2360e6e74925\"},\"description\":\"C\u00e9l\u00e8bre algorithme de Machine Learning, d\u00e9couvrez dans cet article les math\u00e9matiques qui se cachent derri\u00e8re la descente de gradient !\",\"inLanguage\":\"fr-FR\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/datascientest.com\/descente-de-gradient\"]}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/datascientest.com\/#website\",\"url\":\"https:\/\/datascientest.com\/\",\"name\":\"Formation Data Science | DataScientest.com\",\"description\":\"Leader de la formation en Data Science\",\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/datascientest.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"fr-FR\"},{\"@type\":\"Person\",\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/7af2361c48e24e79a8aa2360e6e74925\",\"name\":\"J\u00e9r\u00e9my Robert\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"fr-FR\",\"@id\":\"https:\/\/datascientest.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/jeremyrobert.jpeg\",\"contentUrl\":\"https:\/\/datascientest.com\/wp-content\/uploads\/2023\/11\/jeremyrobert.jpeg\",\"caption\":\"J\u00e9r\u00e9my Robert\"},\"description\":\"J\u00e9r\u00e9my Robert est actuellement Directeur p\u00e9dagogique B2B chez DataScientest.com. 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