Проверка сайта optimizationinpytorch.com - высокая готовность 49%

Домен

optimizationinpytorch.com

Состояние доменного имени ?

Длина домена велика. Но если вы продвигаете запрос, входящий в название домена, то это хорошо.

Домен второго уровня идеален для продвижения.

Исправить

Ответ сервера

200 Успешный ответ

HTTP-код ответа и цепочка редиректов ?

Кол-во редиректов 5 слишком большое! Проверьте настройки сайта и веб-сервера!

Цепочка редиректов:

http://optimizationinpytorch.com 301 MovedPermanently

http://damekdavis.com/STAT-4830 302 Found

http://damek.github.io/STAT-4830 301 MovedPermanently

https://damek.github.io/STAT-4830 301 MovedPermanently

https://damek.github.io/STAT-4830/ 200 OK

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Безопасность

Сайт безопасен

Использование HTTPS и SSL-сертификат ?

На сайте работает защищенный протокол ssl и сайт открывается по https.

Ssl-сертификат действителен до 01.11.2026 2:38:01.

HTTP автоматически перенаправляется на HTTPS.

Поздравляем! Сайт не содержится в реестре РКН.

Кодировка

UTF-8

Кодировка символов страницы ?

Указана кодировка на странице UTF-8.

Язык

en-US

Атрибут lang в HTML-теге ?

Язык документа указан явно: en-US.

Скорость загрузки

~1,26сек

Время отклика сервера (TTFB) ?

Скорость загрузки сайта 1,26сек превышает 1 секунду. Желательно улучшить работу сайта!

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Объем документа

45Кб

Размер HTML-кода страницы ?

Объем html-документа 45Кб оптимален.

Структура html-документа корректна.

Ресурсы

Ресурсы: 8

Внешние ресурсы страницы (CSS, JS, изображения) ?

Кол-во файлов ресурсов 8 достаточно.

Показать полный список ресурсов

Тип	Название	Значение
stylesheet		/STAT-4830/assets/css/style.css?v=1776359778
stylesheet		https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/styles/github.min.css?v=1776359778
stylesheet		/STAT-4830/assets/css/rouge.css?v=1776359778
js		https://cdn.jsdelivr.net/npm/marked/marked.min.js
js		https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min.js
js		https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/python.min.js
js	text/javascript	https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-mml-chtml.js
js		/STAT-4830/assets/js/scale.fix.js

Серверные заголовки

Кол-во: 17

HTTP-заголовки ответа сервера ?

Найдены серверные заголовки 17шт. Подробнее про серверные заголовки.

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Ключ	Значение
Server	GitHub.com
Access-Control-Allow-Origin	*
ETag	"69e11976-b7ba"
Cache-Control	max-age=600
x-proxy-cache	MISS
x-github-request-id	94CE:15BD:738FFBC:748094C:6A8B3583
x-github-edge-region	fra
Accept-Ranges	bytes
Age	0
Date	Sun, 23 Aug 2026 18:01:39 GMT
Via	1.1 varnish
X-Served-By	cache-fra-eddf8230225-FRA
X-Cache	MISS
x-cache-hits	0
x-timer	S1787508099.376186,VS0,VE96
Vary	Accept-Encoding
x-fastly-request-id	7cbfadfdfe2fc22d7012ec01dbcdc402a0dda462

CMS

Jekyll v3.10.0

Система управления сайтом (движок) ?

В мета-теге generator указано: Jekyll v3.10.0.

Веб-сервер

GitHub.com

Программное обеспечение сервера ?

В заголовке Server указано: GitHub.com.

Title

Course Overview | STAT 4830: Numerical Optimization for Data Science and Machine Learning

Заголовок страницы в браузере и поисковой выдаче ?

Необходимо уменьшить число символов в title (текущее значение: 89, оптимально: от 40 до 45)

Дублей словоформ в title не найдено.

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Description

Course materials for STAT 4830

Описание страницы в поисковой выдаче (сниппет) ?

Необходимо увеличить число символов в description (текущее значение мало: 30, минимум: 80, оптимально: от 120 до 130)

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Keywords

Список ключевых слов страницы (устаревший тег) ?

Установите мета-тег keywords!

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Канонический Url

https://damek.github.io/STAT-4830/

Указывает поисковику основную версию страницы ?

Канонический Url прописан корректно.

Robots

Ошибок нет

Директивы для поисковых роботов на уровне страницы ?

Meta-тег robots не указан. Страница свободна для индексации.

Адаптивность

width=device-width, initial-scale=1

Настройка масштабирования на мобильных устройствах ?

Meta-тег viewport со значением-константой width=device-width задаёт ширину страницы в соответствии с размером экрана.

Meta-тег viewport со значением initial-scale=1.0 определяет масштаб 1:1, т.е. «не масштабировать».

Разметка OpenGraph

Кол-во: 6

Мета-теги для красивых превью в соцсетях ?

Разметка OpenGraph задана. Страница оптимизирована под социальные сети.

Показать полный список og мета-тегов

Тип	Значение
og:title	Course Overview
og:locale	en_US
og:description	Course materials for STAT 4830
og:url	https://damek.github.io/STAT-4830/
og:site_name	STAT 4830: Numerical Optimization for Data Science and Machine Learning
og:type	website

Все мета-теги

Кол-во: 11

Полный список мета-тегов страницы ?

Найдены мета-теги 11шт. Мета-теги не видимы для человека и предназначены для обмена информацией между веб-страницей и поисковыми системами, браузерами и другими веб-службами. С ними роботы 🤖 и устройства ведут себя более ожидаемо.

Показать полный список мета-тегов

Тип	Название	Значение
name	viewport	width=device-width, initial-scale=1
name	generator	Jekyll v3.10.0
name	description	Course materials for STAT 4830
name	twitter:card	summary
property	og:title	Course Overview
property	og:locale	en_US
property	og:description	Course materials for STAT 4830
property	og:url	https://damek.github.io/STAT-4830/
property	og:site_name	STAT 4830: Numerical Optimization for Data Science and Machine Learning
property	og:type	website
property	twitter:title	Course Overview

Структура

Ошибок нет

Семантические HTML-элементы страницы ?

Структура документа корректна (теги <html> и <body> присутствуют в единственном экземпляре).

Контент

Ошибок нет

Объём и качество текстового содержимого ?

Слова из title 13 встречаются в тексте достаточно.

Абзацев с текстом 44 достаточно.

Среднее число слов в абзаце 16 достаточно.

Кол-во знаков контента 14607 на странице оптимально.

Кол-во слов 2063 на странице оптимально.

Заголовки

Ошибок нет

Иерархия заголовков H1–H6 ?

На странице присутствуют заголовки <h1> 2. Это прекрасно.

На странице присутствуют заголовки <h2> 7. Это хорошо.

На странице присутствуют заголовки <h3> 7.

Тошнота

6,63

Насколько одно слово доминирует в тексте ?

Тошнота превышает норму 5. Измените текст страницы!

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Академич. тошнота

29,91%

Насколько текст перенасыщен ключевыми словами ?

Академическая тошнота превышает норму 5-15%. Измените текст страницы!

Исправить

Семантическое ядро

20

Наиболее часто встречающиеся слова на странице ?

Контент страницы содержит осмысленный текст и слова.

Показать список слов

Слово	Кол-во	Частота
optimization	44	2,13%
course	26	1,26%
project	24	1,16%
methods	18	0,87%
problems	15	0,73%
learning	13	0,63%
research	10	0,48%
report	10	0,48%
https://github	10	0,48%
numerical	9	0,44%
software	9	0,44%
pytorch	8	0,39%
convex	8	0,39%
machine	7	0,34%
models	7	0,34%
github	6	0,29%
language	6	0,29%
linear	6	0,29%
deliverable	6	0,29%
critique	6	0,29%

Индексирование

Ошибок нет

Разрешено ли индексирование страницы ?

Анкоров на странице 37 оптимально. Поисковые роботы обязательно проиндексируют сайт.

Robots.txt

Найден корректный robots.txt

Файл управления сканированием сайта роботами ?

Кол-во редиректов для файла robots.txt 5 слишком большое! Это может вызывать затруднение при индексации поисковыми роботами!

Проверяемая страница не запрещена в robots.txt.

Robots.txt доступен по постоянному адресу

Цепочка редиректов для файла robots.txt:

http://optimizationinpytorch.com/robots.txt 301 MovedPermanently

http://damekdavis.com/STAT-4830 302 Found

http://damek.github.io/STAT-4830 301 MovedPermanently

https://damek.github.io/STAT-4830 301 MovedPermanently

https://damek.github.io/STAT-4830/ 200 OK

Показать содержимое robots.txt

<!DOCTYPE html>
<html lang="en-US">
  <head>
    <meta charset="UTF-8">
    <meta http-equiv="X-UA-Compatible" content="IE=edge">
    <meta name="viewport" content="width=device-width, initial-scale=1">

<!-- Begin Jekyll SEO tag v2.8.0 -->
<title>Course Overview | STAT 4830: Numerical Optimization for Data Science and Machine Learning</title>
<meta name="generator" content="Jekyll v3.10.0" />
<meta property="og:title" content="Course Overview" />
<meta property="og:locale" content="en_US" />
<meta name="description" content="Course materials for STAT 4830" />
<meta property="og:description" content="Course materials for STAT 4830" />
<link rel="canonical" href="https://damek.github.io/STAT-4830/" />
<meta property="og:url" content="https://damek.github.io/STAT-4830/" />
<meta property="og:site_name" content="STAT 4830: Numerical Optimization for Data Science and Machine Learning" />
<meta property="og:type" content="website" />
<meta name="twitter:card" content="summary" />
<meta property="twitter:title" content="Course Overview" />
<script type="application/ld+json">
{"@context":"https://schema.org","@type":"WebSite","description":"Course materials for STAT 4830","headline":"Course Overview","name":"STAT 4830: Numerical Optimization for Data Science and Machine Learning","url":"https://damek.github.io/STAT-4830/"}</script>
<!-- End Jekyll SEO tag -->

    <link rel="stylesheet" href="/STAT-4830/assets/css/style.css?v=1776359778">
    <!--[if lt IE 9]>
    <script src="https://cdnjs.cloudflare.com/ajax/libs/html5shiv/3.7.3/html5shiv.min.js"></script>
    <![endif]-->
    <!-- start custom head snippets, customize with your own _includes/head-custom.html file -->

<!-- Setup Google Analytics -->



<!-- You can set your favicon here -->
<!-- link rel="shortcut icon" type="image/x-icon" href="/STAT-4830/favicon.ico" -->

<!-- end custom head snippets -->

    <script src="https://cdn.jsdelivr.net/npm/marked/marked.min.js"></script>
    <link rel="stylesheet" href="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/styles/github.min.css?v=1776359778">
    <script src="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/highlight.min.js"></script>
    <script src="https://cdnjs.cloudflare.com/ajax/libs/highlight.js/11.8.0/languages/python.min.js"></script>
    <link rel="stylesheet" href="/STAT-4830/assets/css/rouge.css?v=1776359778">
    <style>
  /* Define base styles */
  :root {
    --base-background-color: #ffffff;
    --base-text-color: #444444;
    --accent-color: #DD4C4F;
    --highlight-color: #D3FFA4;
  }

  body {
    font-family: "AvenirNext-Regular", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
    font-size: 15px;
    background-color: var(--base-background-color);
    color: var(--base-text-color);
    line-height: 1.6;
    margin: 0;
    padding: 0;
    font-weight: 300;
    -webkit-font-smoothing: antialiased;
    -moz-osx-font-smoothing: grayscale;
  }

    /* Image and text wrapper */
  .image-text-wrapper {
    display: block;
    margin-bottom: 1.5em;
    max-width: 100%;
  }

  .image-text-wrapper img {
    float: left;
    max-width: 100%;
    width: auto;
    height: auto;
    margin-right: 20px;
    margin-bottom: 10px;
  }

  .image-text-wrapper div {
    overflow: auto;
    text-align: justify;
  }

  /* Handle images that aren't in text wrappers */
  img {
    max-width: 100%;
    height: auto;
    display: block;
    margin: 1.15em auto;
  }

  /* Style for the wrapper to center the content */
  .wrapper {
    max-width: 650px; /* Maintain content width */
    margin: 0 auto;
    padding: 2em 5%;
    background-color: var(--base-background-color);
    text-align: left;
    font-weight: 300;
  }

  /* Ensure text respects new lines and spaces */
  p, li, a, blockquote {
    white-space: normal;
    word-break: normal;
    margin: 0;
    text-align: left;
  }

  /* Make bold text visibly bold */
  strong, b {
    font-family: "AvenirNext-Medium", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
    font-weight: 600;
  }

  /* Style links to prevent changes on hover */
  a {
    color: var(--accent-color);
    text-decoration: none;
    font-weight: 300; /* Ensure consistent font weight */
  }

  /* Disable font weight change on hover */
  a:hover {
    color: var(--accent-color); /* Keep link color the same on hover */
    text-decoration: none; /* No underline on hover */
    font-weight: 300; /* Explicitly set the font weight to prevent bolding */
  }

  /* Additional styling for headings */
  h1, h2, h3, h4, h5, h6 {
    font-family: "AvenirNext-Medium", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
    margin-top: 1em;
    margin-bottom: 0.5em;
    font-weight: 400;
    scroll-margin-top: 100px;  /* Enough space to clear the header */
  }

  /* Style for blockquotes */
  blockquote {
    color: var(--base-text-color);
    border-left: 4px solid var(--accent-color);
    padding-left: 1em;
    margin: 1em 0;
    font-weight: 300; /* Make blockquotes lighter */
  }

  /* Responsive adjustments for all devices */
  @media screen and (max-width: 768px) {
    body {
      font-size: 14px;
    }

    .wrapper {
      padding: 1em 5%;
    }

    h1, h2, h3, h4, h5, h6 {
      margin-top: 0.75em;
      margin-bottom: 0.5em;
    }

    p, li, blockquote {
      margin: 0.75em 0;
    }
  }

  @media screen and (max-width: 480px) {
    body {
      font-size: 13px;
    }

    .wrapper {
      padding: 1em;
    }

    em, i {
      font-weight: 500;
    }

    p, li, blockquote {
      margin: 0.5em 0;
    }
  }

  /* Ensure content is always visible and scrollable */
  html, body {
    overflow-x: hidden;
    width: 100%;
    -webkit-overflow-scrolling: touch;
  }

  /* Improve touch and click targets on mobile */
  a, button {
    min-height: 44px;
    min-width: 44px;
  }

  /* Improve readability on high-DPI screens */
  @media (-webkit-min-device-pixel-ratio: 2), (min-resolution: 192dpi) {
    body {
      -webkit-font-smoothing: subpixel-antialiased;
    }
  }

  /* Add styles for dynamic content */
  .course-content {
    margin-top: 2em;
    color: var(--base-text-color);
  }

  .course-content h1,
  .course-content h2,
  .course-content h3,
  .course-content h4,
  .course-content h5,
  .course-content h6 {
    color: var(--base-text-color);
    font-family: "AvenirNext-Medium", -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif;
  }

  .course-content a {
    color: var(--accent-color);
    text-decoration: none;
    font-weight: 300;
  }

  .course-content a:hover {
    color: var(--accent-color);
    text-decoration: none;
    font-weight: 300;
  }

  .course-content p {
    margin: 1.15em 0;
    line-height: 1.55;
  }

  .course-content ul,
  .course-content ol {
    margin: 1.15em 0;
    padding-left: 1.75em;
    list-style-position: outside;
  }

  .course-content li {
    margin: 0;
    line-height: 1.4;
    padding-left: 0.2em;
  }

  .course-content li p {
    margin: 0;
  }

  .course-content h1,
  .course-content h2,
  .course-content h3,
  .course-content h4 {
    margin-top: 1.5em;
    margin-bottom: 0.5em;
  }

  /* Handle indented lists */
  .course-content ul ul,
  .course-content ul ol,
  .course-content ol ul,
  .course-content ol ol {
    margin: 0;
    padding-left: 1.2em;
  }

  /* Ensure proper alignment of list markers */
  .course-content ul {
    list-style: disc outside none;
  }

  .course-content ul ul {
    list-style-type: circle;
  }

  /* Keep blockquote styles */
  blockquote {
    margin: 1em 0;
    padding: 0 1em;
    color: #656d76;
    border-left: 0.25em solid #DD4C4F;
  }

  blockquote > :first-child {
    margin-top: 0;
  }

  blockquote > :last-child {
    margin-bottom: 0;
  }

  /* Update header styles for floating */
  .page-header {
    position: fixed;
    top: 0;
    left: 0;
    right: 0;
    width: 100%;
    z-index: 1000;
    background: rgba(255, 255, 255, 0.9);
    backdrop-filter: blur(5px);
    border-bottom: none;
  }

  /* Add inner container for header content */
  .header-content {
    max-width: 650px;
    margin: 0 auto;
    padding: 1em 5%;  /* Match wrapper padding */
  }

  /* Wrapper styles */
  .wrapper {
    max-width: 650px;
    margin: 0 auto;
    padding: 2em 5%;
  }

  /* Mobile adjustments */
  @media screen and (max-width: 768px) {
    .header-content {
      padding: 1em 5%;  /* Keep consistent padding */
    }
    
    .page-header .title {
      font-size: 0.9em;
      line-height: 1.4;
    }
    
    .page-header .links {
      font-size: 0.85em;
      margin-top: 0.5em;
    }
  }

  @media screen and (max-width: 480px) {
    .header-content {
      padding: 1em 5%;  /* Keep consistent padding */
    }
  }

  /* Remove sidebar-related margin */
  .wrapper {
    margin: 0 auto;
    max-width: 650px;
    padding: 2em 5%;
  }

  /* Remove all sidebar-nav related styles */
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    display: none;
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  /* Code block styles - GitHub style */
  pre {
    margin: 1em 0;
    padding: 16px;
    background-color: #f6f8fa;
    border: 1px solid #d0d7de;
    border-radius: 0;
    font-size: 85%;
    line-height: 1.45;
    overflow: auto;
    word-wrap: normal;
    white-space: pre;
  }

  pre code {
    padding: 0;
    margin: 0;
    border: 0;
    font-family: ui-monospace,SFMono-Regular,SF Mono,Menlo,Consolas,Liberation Mono,monospace;
    font-size: inherit;
    line-height: inherit;
    word-wrap: normal;
    white-space: pre;
    background-color: transparent;
  }

  /* Override highlight.js GitHub theme colors to match exactly */
  .hljs {
    background: #f6f8fa;
    color: #24292e;
  }

  /* Code block styles */
  .code-wrapper {
    position: relative;
    margin: 0;
  }

  /* Copy button styles - centered icons and compact box */
  .copy-button {
    position: absolute;
    top: 8px;
    right: 8px;
    padding: 2px;
    border: none;
    border-radius: 0;
    cursor: pointer;
    background: transparent;
    transition: background-color 0.2s;
    display: flex;
    align-items: center;
    justify-content: center;
    width: 24px;
    height: 24px;
  }

  .copy-button:hover {
    background-color: #e0e0e0;
  }

  /* Copy icon styles - centered */
  .copy-button svg {
    width: 14px;
    height: 14px;
    fill: #57606a;
  }

  /* Keep the rest of your copy button styles the same */
  .copy-button .copy-icon {
    display: block;
  }

  .copy-button .check-icon {
    display: none;
    fill: #1a7f37;
  }

  .copy-button.copied .copy-icon {
    display: none;
  }

  .copy-button.copied .check-icon {
    display: block;
  }

  /* Rouge highlight wrapper: keep gray background consistently */
  .highlight {
    background: #f6f8fa;
    border: 1px solid #d0d7de;
    padding: 16px;
    margin: 1em 0;
  }

  .highlight pre {
    margin: 0;
    padding: 0;
    background: transparent;
    border: 0;
  }

  /* Add scroll margin to headings to account for fixed header */
  h1, h2, h3, h4, h5, h6 {
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          <div class="title">STAT 4830: Numerical Optimization for Data Science and Machine Learning - <a href="https://damekdavis.com">Damek Davis</a></div>
          <div class="links">
            <a href="/STAT-4830/toc.html">Table of contents</a> | 
            <a href="/STAT-4830/index.html">Course overview</a> | 
            <a href="https://github.com/damek/STAT-4830">View on Github</a>
          </div>
        </div>
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      <div class="content-wrapper" style="margin-top: 8em;">
        <h1 id="stat-4830-numerical-optimization-for-data-science-and-machine-learning">Stat 4830: Numerical optimization for data science and machine learning</h1>

<p>AKA: Optimization in PyTorch</p>

<p>For lecture notes see <a href="/STAT-4830/toc.html">table of contents</a>.</p>

<p><strong>Office Hours:</strong> Tuesdays 12:30-1:30 PM</p>

<h2 id="table-of-contents">Table of contents</h2>
<ul>
  <li><a href="#high-level-thoughts-on-the-course">High-level thoughts on the course</a></li>
  <li><a href="#overview">Overview</a></li>
  <li><a href="#pre-requisites">Pre-requisites</a></li>
  <li><a href="#deliverable-a-final-project-due-on-week-4">Deliverable: a final project due on week 4</a></li>
  <li><a href="#textbooks-readings-and-software-libraries">Textbooks, readings, and software libraries</a></li>
  <li><a href="#brief-historical-perspective-on-optimization">Brief historical perspective on optimization</a></li>
</ul>

<h2 id="high-level-thoughts-on-the-course">High-level thoughts on the course</h2>

<ul>
  <li>
    <p><strong>Why am I excited about this course?</strong> Optimization works! Everything you learn about solving optimization problems numerically will be useful in your career, whether you’re a data scientist, AI researcher, or an engineer of any kind. Understanding how optimization methods work and how to use them will actually help you solve <em>real</em> problems.</p>

    <p>To quote <a href="https://x.com/jachiam0/status/1872849427653902744">Joshua Achiam</a> (OpenAI):</p>
    <blockquote>
      <p>If you want to know something deep, fundamental, and maximally portable between virtually every field: study mathematical optimization.</p>
    </blockquote>

    <p><img src="/STAT-4830/figures/achiam_tweet.png" alt="Joshua Achiam's tweet about mathematical optimization" /></p>
  </li>
  <li><strong>Who is this course meant for?</strong> This is an experimental undergraduate course meant for students who are (roughly) in their junior or senior year. The course should also be beneficial to PhD students who wish to apply optimization techniques in their research.</li>
  <li><strong>What is the goal of the course?</strong> By the end of the course, my goal is for you to be able to <em>intelligently apply numerical optimization techniques</em> in a research project in machine learning, data science, or related fields. We will discuss optimization theory in the course, but that will not be the focus.</li>
  <li><strong>Production vs. Research-level code?</strong> We will mainly be coding Python notebooks developing research-level code that focuses on the intricacies of optimization methods. Taking research-level code to production is a separate skill that we will not focus on in this course.</li>
  <li><strong>Are there similar courses at Penn or other universities?</strong> Not that I am aware of—if you find some, let me know! I will develop this course from scratch and adapt it to student interests as we go.</li>
  <li><strong>Which IDE should I use?</strong> For local development, use <a href="https://www.cursor.com/">Cursor</a>–it’s free for students with a .edu address. For remote development, use <a href="https://colab.research.google.com/">Google Colab</a>.</li>
</ul>

<h2 id="official-syllabus">Official Syllabus</h2>

<blockquote>
  <p>See <a href="/STAT-4830/section/0/notes.html#tentative-course-structure">tentative course schedule</a> for the tentative course schedule.</p>
</blockquote>

<p>Optimization is the modeling language in which modern data science, machine learning, and sequential decision-making problems are formulated and solved numerically. This course will teach you how to formulate these problems mathematically, choose appropriate algorithms to solve them, and implement and tune the algorithms in PyTorch. Tentative topics include:</p>
<ul>
  <li>Optimization-based formulations of statistical estimation and inverse problems in data science; predictive and generative models in machine learning; and control, bandit, and reinforcement learning problems in sequential decision-making.</li>
  <li>A high-level tour of the foundations of mathematical optimization, viewed as an algorithmic discipline, and what to expect from theory; key considerations such as convexity, smoothness, saddle points, and stochasticity; classical formulations, such as linear, quadratic, and semidefinite programs; numerical solvers such as CVXPY.</li>
  <li>Popular optimization methods such as (online and stochastic) gradient methods, (quasi) Newton methods, algorithmic extensions to constrained, regularized, and distributed problems, as well as optimization methods that preserve privacy of sensitive data.</li>
  <li>Modern software libraries such as PyTorch and Jax and the principles underlying “automatic differentiation” techniques. Best practices in tuning optimization methods, e.g., in deep learning problems.</li>
</ul>

<p>By the end of this course, you will become an intelligent consumer of numerical methods and software for solving modern optimization problems.</p>

<h2 id="pre-requisites">Pre-requisites</h2>
<ul>
  <li>Basic calculus and linear algebra (Math 2400)</li>
  <li>Basic Probability (Stat 4300)</li>
  <li>Programming experience in a scripting language such as Python. Basic comfort in iteration and functions.</li>
</ul>

<h2 id="assessment">Assessment</h2>

<ul>
  <li>In class participation and attendance (starting Thur March 20th) (5%)</li>
  <li>Final project report, implementation, and development process (65%)
    <ul>
      <li>Implementation (25%)</li>
      <li>Report / self critiques (25%)</li>
      <li>Team peer assessment (5%)</li>
      <li>Instructor assessment of involvement in project (10%)</li>
    </ul>
  </li>
  <li>Midterm project presentation (10%)</li>
  <li>Final project presentation (20%)</li>
</ul>

<h2 id="final-project-deliverable-due-on-week-4">Final project deliverable due on week 4</h2>

<p>VERY detailed instructions on how to get started with your project are available at the following link: <a href="https://github.com/damek/STAT-4830-project-base">STAT-4830-project-base</a></p>

<h3 id="timeline-and-milestones">Timeline and milestones</h3>

<p>Deliverables (Due Fridays):</p>
<ul>
  <li>Week 2 (Jan 23): Email Project Team Names to Ai, Jiahao <a href="mailto:jiahaoai@wharton.upenn.edu">jiahaoai@wharton.upenn.edu</a></li>
  <li>Week 4 (Feb 6): Report Draft 1 + Code + Self Critique</li>
  <li>Week 5 (Feb 13): Slides Draft 1</li>
  <li>Week 6 (Feb 20): Report Draft 2 + Code + Self Critique</li>
  <li>Week 7 (Feb 27): Slides Draft 2</li>
  <li>Week 8: ⚡ Lightning Talks in Class (Mar 3/5) &amp; Report Draft 3 due Friday ⚡</li>
  <li>Spring Break (Mar 7-15)</li>
  <li>Week 9 (Mar 20): Slides Draft 3</li>
  <li>Week 10 (Mar 27): Report Draft 4 + Code + Self Critique</li>
  <li>Week 11 (Apr 3): Slides Draft 4</li>
  <li>Week 12 (Apr 10): Report Draft 5 + Code + Self Critique</li>
  <li>Week 13 (Apr 17): Slides Draft 5</li>
  <li>Week 14 (Apr 21/23): Final Presentations in Class</li>
  <li>Week 15 (Apr 28): Final Report + Code + Self Critique</li>
</ul>

<p>Note: Instructions for peer feedback will be added throughout the semester for each deliverable.</p>

<p><strong>Why this approach?</strong><br />
Final projects often become a single rushed deliverable. We’ll break the project into regular drafts and feedback cycles so your team can iterate, improve, and build something more substantial and refined. You’ll have multiple checkpoints, each with opportunities for critique and revision. By the end, you’ll have a polished piece of work you can showcase—something worthy of your portfolio or internship applications.</p>

<h3 id="deliverable-format">Deliverable format</h3>

<ol>
  <li><strong>GitHub repository</strong>
    <ul>
      <li>Centralize all materials: your written report, code, and presentation slides.</li>
      <li>Be sure to include a clear README with instructions for reproducing results.</li>
    </ul>
  </li>
  <li><strong>Executable demo</strong>
    <ul>
      <li>Provide a runnable demonstration in Google Colab. If your overall code is extensive, create a minimal Colab notebook that shows core functionality or key results.</li>
    </ul>
  </li>
  <li><strong>Written report</strong>
    <ul>
      <li>By default, structure it like a short conference-style paper (e.g., 8 pages + supplementary).</li>
      <li>If you have a more creative format in mind, just run it by me first.</li>
    </ul>
  </li>
</ol>

<h3 id="feedback-loop">Feedback loop</h3>

<ul>
  <li>I will meet with each group semi-weakly to discuss project scope and direction, reflect on progress and address challenges, and check in before deliverable are due.</li>
  <li>Additional questions are welcome anytime.</li>
</ul>

<h3 id="rules">Rules</h3>

<ul>
  <li><strong>Group size</strong>: 3–4 students. This fosters collaboration while keeping the workload balanced.</li>
  <li><strong>LLM usage</strong>: You should use large language models in your work to help with writing, brainstorming, and coding. But verify outputs critically—don’t rely on them blindly.</li>
</ul>

<p>By developing your projects in iterative steps, you will receive feedback multiple times and have a better chance of creating something valuable. This also help me shape the course content based on your areas of interest, ensuring that lectures and assignments align well with your goals.</p>

<!-- * **Homework (20%)**. There will be approximately two homework assignments on which you will demonstrate your understanding of the theory and programming components of the course. Gradescope will be used for homework submission and grading.
* **Quizzes (20%)**. Regular quizzes will be administered throughout the course. 
* **Course project (60%)**. Students will work together in groups of 3-5 students. The size of the team will be taken into account when assigning grades. Larger teams must have more substantial projects. Project teams will be formed in the first four weeks of the semester. There are a series of milestones. 
  * (10%) Initial project proposal.
  * (10%) Midterm project presentation. 
  * (40%) Final project report, presentation, and software deliverable (details below). -->

<h3 id="course-project-ideas">Course project ideas</h3>
<p>In the course project, you will apply the optimization skills you learned in the course. For example, your final project could include:</p>
<ul>
  <li>Training/fine-tuning a model: A detailed write-up of your strategy for training or fine-tuning a model (e.g., language, code, math, or vision model). Describe failures, successes, and rabbit holes. Illustrate the use of the final model. Use GPUs to scale up. Compare multiple optimization methods and choose one with the “best” performance.</li>
  <li>Build a useful, novel <a href="https://app.primeintellect.ai/dashboard/environments?ex_sort=by_sections">RL environment</a> on Prime Intellect’s environment hub. Demonstrate that performing RL on the environment leads to desired behavior.</li>
  <li>Reproducibility: A detailed write-up of your attempt to reproduce, falsify, or improve numerical results from the optimization literature.</li>
  <li>Augmenting an existing research project: Let’s say you’re already working on a research project with Penn faculty that includes an optimization component. We can likely find a way to align your project in the course with your research project by improving the optimization component of your project. We must discuss a bit to ensure the optimization component is extensive enough for course credit.</li>
  <li>Improving optimizers on an existing/new benchmark: Several benchmarks have recently been proposed for optimization methods in ML. For example, (1) in <a href="https://github.com/KellerJordan/modded-nanogpt">Modded-NanoGPT repo</a>, some independent researchers are attempting to train small versions of GPT as fast as possible; (2) in <a href="https://github.com/mlcommons/algorithmic-efficiency">the AlgoPerf repo</a> the ML Commons project is benchmarking optimization methods for training deep learning models. A potential project is to improve existing methods on such benchmarks or develop your own and set the initial records.</li>
  <li>Educational tools and software: Educational resources illustrating advanced concepts related to but not covered in the course material. The project should be polished: the instructor should be comfortable including the deliverable in future versions of the course with little to no modification.</li>
  <li>AI for math software:
    <ul>
      <li>In research, we often need to prove or disprove inequalities of the form $LHS(x) \leq RHS(x)$ for some variable $x$. One way to do this is to use optimization software to minimize $RHS(x) - LHS(x)$. If the value is less than zero, than we’ve disproved the inequality. It would be highly useful to develop software that can do this automatically with optimization methods.  Often these are difficult nonconvex optimization problems so you’ll have to use all the tricks from the course to solve them + use an LLM to formulate the problem or relaxations thereof. This would be really cool to have!</li>
    </ul>
  </li>
  <li>AutoOPT tools: Combined with an LLM, automatically formulate and tune optimization methods for a given task.</li>
</ul>

<p>I will post more project ideas adapted to student interests in the course’s first weeks. Each project must include a Google Colab (or equivalent) walkthrough of your results and claims. I must approve the scope of the project.</p>

<h2 id="textbooks-readings-and-software-libraries">Textbooks, readings, and software libraries</h2>
<p>This course material will be self-contained outside of the prerequisites, but there will be no official textbook. Some material will draw on recent research published in academic conferences and journals. Some will draw on software libraries that are mature or in development. Below, I have instead listed several resources that we may draw – more will be added throughout the course:</p>

<h3 id="optimization">Optimization</h3>

<h4 id="general-background">General background</h4>

<ol>
  <li>
    <p>Beck, A. (2014). Introduction to nonlinear optimization: Theory, algorithms, and applications with MATLAB. Society for Industrial and Applied Mathematics.</p>
  </li>
  <li>
    <p>Nocedal, J., &amp; Wright, S. J. (1999). Numerical optimization. Springer.</p>
  </li>
  <li>
    <p>Boyd, S., &amp; Vandenberghe, L. (2004). Convex optimization. Cambridge University Press.</p>
  </li>
  <li>
    <p>Hazan, E. (2016). Introduction to online convex optimization. Foundations and Trends® in Optimization, 2(3-4), 157-325.</p>
  </li>
  <li>
    <p>UCLA course ECE236C - Optimization Methods for Large-Scale Systems
<a href="https://www.seas.ucla.edu/~vandenbe/ee236c.html">https://www.seas.ucla.edu/~vandenbe/ee236c.html</a></p>
  </li>
</ol>

<h4 id="numerical-optimization-in-machine-learning">Numerical optimization in machine learning</h4>

<ol>
  <li>
    <p>Google Research. (n.d.). Deep learning tuning playbook.
<a href="https://github.com/google-research/tuning_playbook">https://github.com/google-research/tuning_playbook</a></p>
  </li>
  <li>
    <p>Google Research. (2023). Benchmarking neural network training algorithms and the ML commons library.
<a href="https://arxiv.org/abs/2306.07179">https://arxiv.org/abs/2306.07179</a>
<a href="https://github.com/mlcommons/algorithmic-efficiency/tree/main">https://github.com/mlcommons/algorithmic-efficiency/tree/main</a></p>
  </li>
  <li>
    <p>Moreau, T., et al. (2022). Benchopt: Reproducible, efficient and collaborative optimization benchmarks.
<a href="https://github.com/benchopt/benchopt">https://github.com/benchopt/benchopt</a></p>
  </li>
  <li>
    <p>Schmidt, R., et al. (2021). Descending through a Crowded Valley - Benchmarking Deep Learning Optimizers.
<a href="https://proceedings.mlr.press/v139/schmidt21a">https://proceedings.mlr.press/v139/schmidt21a</a></p>
  </li>
</ol>

<h3 id="software-and-tutorials">Software and tutorials</h3>

<h4 id="convex-optimization-in-python-cvxpy">Convex optimization in Python: CVXPY</h4>

<p>CVXPY: Convex optimization, for everyone.
<a href="https://www.cvxpy.org/">https://www.cvxpy.org/</a></p>

<h4 id="pytorch-jax-and-auto-differentiation">PyTorch, Jax, and auto differentiation</h4>

<ol>
  <li>
    <p>PyTorch (The full library): <a href="https://pytorch.org/">https://pytorch.org/</a></p>
  </li>
  <li>
    <p>Numerical implementation of optimizers in PyTorch:
<a href="https://pytorch.org/docs/stable/optim.html#algorithms">https://pytorch.org/docs/stable/optim.html#algorithms</a></p>
  </li>
  <li>
    <p>Jax library: <a href="https://github.com/google/jax">https://github.com/google/jax</a></p>
  </li>
  <li>
    <p>Micrograd: A tiny educational “auto differentiation” library
<a href="https://github.com/karpathy/micrograd">https://github.com/karpathy/micrograd</a></p>
  </li>
</ol>

<h4 id="scalable-linear-algebra">Scalable linear algebra</h4>

<p>CoLA: a framework for scalable linear algebra that exploits structure often found in machine learning problems.
<a href="https://github.com/wilson-labs/cola">https://github.com/wilson-labs/cola</a></p>

<h4 id="transformers-and-diffusion-models">Transformers and diffusion models</h4>

<ol>
  <li>
    <p>MinGPT: A PyTorch re-implementation of GPT
<a href="https://github.com/karpathy/minGPT">https://github.com/karpathy/minGPT</a></p>
  </li>
  <li>
    <p>The annotated diffusion model
<a href="https://huggingface.co/blog/annotated-diffusion">https://huggingface.co/blog/annotated-diffusion</a></p>
  </li>
  <li>
    <p>Repository containing resources and papers for diffusion models
<a href="https://diff-usion.github.io/Awesome-Diffusion-Models/">https://diff-usion.github.io/Awesome-Diffusion-Models/</a></p>
  </li>
</ol>

<h4 id="version-control-git-and-github">Version control: git and github</h4>

<p>GitHub Docs: Hello World
<a href="https://docs.github.com/en/get-started/start-your-journey/hello-world">https://docs.github.com/en/get-started/start-your-journey/hello-world</a></p>

<h4 id="training-visualization">Training visualization</h4>

<p>Weights and Biases
<a href="https://wandb.ai/site">https://wandb.ai/site</a></p>

<h4 id="puzzles">Puzzles!</h4>

<p>Sasha Rush’s has luckily made a series of open source puzzles for helping you understand GPUs, automatic differentiation, and optimization.</p>
<ol>
  <li>
    <p>Tensor puzzles: https://github.com/srush/Tensor-Puzzles</p>
  </li>
  <li>
    <p>GPU Puzzles: https://github.com/srush/GPU-Puzzles</p>
  </li>
  <li>
    <p>Autodiff Puzzles: https://github.com/srush/Autodiff-Puzzles/</p>
  </li>
</ol>

<h1 id="brief-historical-perspective-on-optimization">Brief historical perspective on optimization</h1>

<p>It’s useful to appreciate how optimization evolved as an algorithmic discipline over the last seventy years:</p>

<ul>
  <li>Mid-20th Century: Linear Programming emerged as a critical tool in operations research, fueled by George Dantzig’s simplex method. This was pivotal for industrial logistics, military planning, and resource allocation.</li>
  <li>1960s–1990s: Convex optimization grew more important, driven by work on gradient-based methods, interior-point methods, and software that could solve large-scale linear and convex problems.</li>
  <li>2000s: Tools like CVX (MATLAB-based) made formulating and solving standard convex problems more accessible to a broad audience—i.e., “specify your problem in a solver-friendly language, and let the solver handle it.”</li>
  <li>Modern Era: Deep learning frameworks (e.g., PyTorch, TensorFlow, Jax) have shifted the emphasis to a “build and iterate” approach. Instead of specifying problems in a polished convex form, we often “get our hands dirty” with nonconvex models, direct gradient-based methods, and custom loss functions. This iterative exploration is precisely what enabled the explosion of large language models (LLMs) and other powerful neural architectures.</li>
</ul>

<p>In this course, we will appreciate both sides: solver-based approaches for classical, well-structured problems (via CVXPY) and more flexible, high-powered frameworks (via PyTorch) for data-driven, nonconvex tasks.</p>

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