Modeled on Princeton COS 511 (Theoretical ML)

机器学习理论:PAC、Boosting 与在线学习

Learning Theory: PAC, Boosting & Online Learning

Hand-derive PAC bounds, hand-build AdaBoost, hand-run regret curves — turn learning theory from formulas into experiments you run

7 labs12 AI-mentored sessions~6 hoursBilingual · EN / 中
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About this course

A derive-it-and-build-it theory course: no memorizing theorems, no proof drills. In every
session an AI mentor walks you through a few lines of numpy, fixes a random seed, and runs
out a curve — then you look back and see that curve landing exactly inside the bound the
theorem promised. We start from "what does learnable even mean" and verify PAC sample
complexity with your own Monte-Carlo runs; use shattering and VC dimension to measure how
expressive a hypothesis class really is; hand-build AdaBoost from scratch and watch training
error decay exponentially while margins march rightward; and finally enter online learning —
weighted majority, multiplicative weights, regret minimization — watching average regret
vanish at the √(logN / T) rate. Theory here isn't chalkboard symbols; it's real,
checkable experiments in your sandbox: formulas are typeset for you, shattering is drawn as
cells, and you drag the knobs on the regret curve yourself. You'll end up actually believing
these bounds — because every one of them, you made hold with your own hands.

What you'll learn

  • Verify PAC sample complexity with your own Monte-Carlo runs, and explain what (ε, δ) actually guarantees
  • Count a hypothesis class's shattering power, pin down its VC dimension, and read the VC generalization bound
  • Hand-build AdaBoost from scratch and watch training error decay exponentially while margins shift right
  • Implement Weighted Majority and Multiplicative Weights (Hedge), pushing mistakes and regret inside the theorem's bound
  • Plot regret curves and explain why average regret vanishes at the √(logN / T) rate
  • Explain how online learning, Boosting and game theory all rest on the same no-regret idea

Syllabus

1PAC Foundations: What Does Learnable Mean3 sessions
  • 1What Does Learnable Mean: The PAC Framework30 minStart →
  • 2Sample Complexity: How Many Samples a Finite Class Needs30 minStart →
  • 3Agnostic Learning & Uniform Convergence: Coping with Noise30 minStart →
2VC Dimension: Measuring a Class's Expressive Power3 sessions
  • 1Shattering: How Many Labelings a Class Can Realize30 minStart →
  • 2VC Dimension: Definition and Classic Values30 minStart →
  • 3Growth Function, Sauer's Lemma & the VC Generalization Bound30 minStart →
3Boosting: From Weak to Strong, Build AdaBoost by Hand3 sessions
  • 1Weak-to-Strong: The Wisdom of Weak Voters30 minStart →
  • 2Build AdaBoost from Scratch30 minStart →
  • 3Exponential Training-Error Decay, Margins & Generalization30 minStart →
4Online Learning: Weighted Majority & Regret Minimization3 sessions
  • 1The Online Learning Framework & the Halving Algorithm30 minStart →
  • 2Weighted Majority: When No Expert Is Perfect30 minStart →
  • 3Multiplicative Weights (Hedge) & Regret30 minStart →
5Online Convex Optimization: Regret Bounds of Gradient Descent0 sessions

Sessions are on the way.

6Bandits: The Explore-Exploit Tradeoff0 sessions

Sessions are on the way.

7Learning & Games: No-Regret Dynamics & Minimax0 sessions

Sessions are on the way.

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