{
  "schema": "ml-prep/item@1",
  "item": {
    "id": "mit-6-036-s2019-midterm-q5",
    "area": "machine-learning",
    "topic": "optimization",
    "origin": "external",
    "title": "Learning as optimization",
    "skills": [
      "objective-functions",
      "convexity",
      "optimization-diagnostics",
      "stationary-points"
    ],
    "priority": "core",
    "difficulty": "medium",
    "estimated_minutes": 18,
    "prerequisites": [
      "derivatives",
      "gradient-descent",
      "loss-functions"
    ],
    "source_id": "mit-6-036-exams",
    "locator": {
      "document": "Spring 2019 Midterm Exam",
      "label": "Question 5: Learning as Optimization",
      "page_label": "problem PDF pp. 15–16",
      "solution_pages": "15–16"
    },
    "links": {
      "problem": "https://introml.mit.edu/_static/spring23/midterm/review/midterm_spring2019.pdf#page=15",
      "solution": "https://introml.mit.edu/_static/spring23/midterm/review/midterm_solutions_spring2019.pdf#page=15"
    },
    "selection_note": "Derives an update and distinguishes slow, oscillating, and divergent learning-rate behavior from objective geometry.",
    "answer_status": "official-solution"
  }
}